additive number theory

Abstractly, additive number theory includes the study of abelian groups and commutative semigroups with an addition operation.

Two principal objects of study in additive number theory are the sumset A#43;B#61;#92;#123;a#43;b#58;a#92;inA,b#92;inB#92;#125; of two subsets A and B of elements from an abelian group G, and the h-fold sumset of A, hA#61;#92;underset#123;h#125;#123;#92;underbrace#123;A#43;#92;cdots#43;A,.}}

Additive number theory has close ties to combinatorial number theory and the geometry of numbers.

1966 [Macmillan], W. E. Deskins, Abstract Algebra, 1995, Dover, page 152,
One of the famous theorems of additive number theory states that each positive integer is expressible in at least one way as the sum of the squares of not more than four positive integers.

The Circle Method is a beautiful idea for studying many problems in additive number theory. It originated in investigations by Hardy and Ramanujan [HR] on the partition function P(n), the number of ways we can write n as a sum of positive integers. Since then it has been used to study problems in additive number theory ranging from writing numbers as sums of primes or k#92;mathsf#123;th#125; powers (for fixed k) to trying to count how many twin primes there are less than x.

2006, Steven J. Miller, Ramin Takloo-Bighash, An Invitation to Modern Number Theory, Princeton University Press, page 303:

Additive number theory is a very broad area within which lies the theory of partitions, and the subject of representation of integers as sums of squares, cubes, etc. There is a vast literature in additive number theory on problems of the following type: Given a subset A of the integers, when does it form a basis for the integers? That is, when can every positive integer be expressed as the sum of at most a (fixed) bounded number of elements of A?

2008, Krishnaswami Alladi, editor, Surveys in Number Theory, Springer, page ix:

(number theory) The subfield of number theory concerning the behaviour of sumsets (integer sets added to each other elementwise).


geometry of numbers

The field was initiated by German mathematician Hermann Minkowski (1910, Geometrie der Zahlen).

A typical approach in the geometry of numbers is to view a ring of algebraic integers as a lattice in #92;textstyle#92;mathbb#123;R#125;ⁿ; the study of these lattices provides fundamental information on algebraic numbers.

1969, C. G. Lekkerkerker, Geometry of Numbers, Wolters-Noordoff, North-Holland, page 1,
The geometry of numbers to which this book is devoted deals with arbitrary bodies and arbitrary lattices in the n-dimensional euclidean space. Its aim is to study various quantities describing the behaviour of a body with respect to a lattice.

2000, C. D. Olds, Anneli Lax, Giuliana Davidoff, The Geometry of Numbers, Mathematical Association of America:

2006, Enrico Bombieri, Walter Gubler, Heights in Diophantine Geometry, Cambridge University Press, page 181,
The easy proof is obtained applying the pigeon-hole principle to
α₁x_1+…+αₙx_n(mod 1)|x_i=0,…N,
or by geometry of numbers by applying Minkowski's first theorem in C.2.19 to the symmetric convex body of volume 2ⁿ⁺¹ given by
|X_0+α₁X_1+…αₙX_n|<N⁻ⁿ,|X_i|<N,i=1,…N.

(number theory) The subbranch of number theory which applies techniques from geometry to the study of algebraic numbers.


梅森素數

ㄇㄟˊ ㄙㄣ ㄙㄨˋ ㄕㄨˋ

Мэйсэнь сушу

/meɪ̯³⁵ sən⁵⁵ su⁵¹⁻⁵³ ʂu⁵¹/

/muːi̯²¹ sɐm⁵⁵ sou̯³³ sou̯³³/

/meɪ̯³⁵ sən⁵⁵ su⁵¹⁻⁵³ ʂu⁵¹/

/muːi̯²¹ sɐm⁵⁵ sou̯³³ sou̯³³/


Chinese remainder theorem

the Chinese remainder theorem (canonical)

The earliest known formulation of the theorem was in the Chinese Sun Zi's Mathematical Manual circa 400 AD.

(number theory) A theorem stating that, if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.

Chinese remainder theorem
Sunzi Suanjing


computational number theory

Topics studied in computational number theory include algorithms for primality testing and integer factorisation, finding solutions to Diophantine equations and explicit methods in arithmetic geometry.

Computational number theory has applications in cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis.

1990, Carl Pomerance, editor, Proceedings of Symposia in Applied Mathematics, Volume 42: Cryptology and Computational Number Theory, American Mathematical Society:

1994, Hari Krishna, Bal Krishna, Kuo-Yu Lin, Jenn-Dong Sun, Computational Number Theory and Digital Signal Processing: Fast Algorithms and Error Control Techniques, CRC Press, https://books.google.com.au/books?id=8u1kx3peO6AC&printsec=frontcover&dq=%22computational+number+theory%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiy0c_SnvjuAhUCyjgGHUIkBnUQ6AEwB3oECCUQAg#v=onepage&q=%22computational%20number%20theory%22&f=false.

2001, Kazimierz Alster, Jerzy Urbanowicz, Hugh C. Williams, editors, Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference, Walter de Gruyter:

(mathematics, number theory) The field of study dealing with computational methods for investigating and solving problems in number theory and arithmetic geometry.

théorie algorithmique des nombres

field of study dealing with computational methods in number theory


antiprime

highly composite number
highly composite number#English

(number theory) Synonym of highly composite number


restklasse

head

restklasse c (singular definite restklassen, plural indefinite restklasser)

restklassen (definite singular)
restklasser (indefinite plural)

Analysable as rest (“residue”) + klasse.


liczba dodatnia

liczba dodatnia (nominative singular)
liczby dodatnie (nominative plural)
liczby dodatniej (genitive singular)
liczb dodatnich (genitive plural)
liczbie dodatniej (dative singular)
liczbom dodatnim (dative plural)
liczbę dodatnią (accusative singular)
liczby dodatnie (accusative plural)
liczbą dodatnią (instrumental singular)
liczbami dodatnimi (instrumental plural)
liczbie dodatniej (locative singular)
liczbach dodatnich (locative plural)
liczbo dodatnia (singular vocative)
liczby dodatnie (plural vocative)


liczba ujemna

liczba ujemna (nominative singular)
liczby ujemne (nominative plural)
liczby ujemnej (genitive singular)
liczb ujemnych (genitive plural)
liczbie ujemnej (dative singular)
liczbom ujemnym (dative plural)
liczbę ujemną (accusative singular)
liczby ujemne (accusative plural)
liczbą ujemną (instrumental singular)
liczbami ujemnymi (instrumental plural)
liczbie ujemnej (locative singular)
liczbach ujemnych (locative plural)
liczbo ujemna (singular vocative)
liczby ujemne (plural vocative)


kongruencja

kongruencja (nominative singular)
kongruencje (nominative plural)
kongruencji (genitive singular)
kongruencji (genitive plural)
kongruencyj (archaic genitive plural)
kongruencji (dative singular)
kongruencjom (dative plural)
kongruencję (accusative singular)
kongruencje (accusative plural)
kongruencją (instrumental singular)
kongruencjami (instrumental plural)
kongruencji (locative singular)
kongruencjach (locative plural)
kongruencjo (singular vocative)
kongruencje (plural vocative)

Learned borrowing from Latin congruentia.

lbor

(number theory) congruence (relation indicating two numbers give the same remainder when divided by some number)


孿生質數

ㄌㄨㄢˊ ㄕㄥ ㄓˋ ㄕㄨˋ

ㄌㄨㄢˊ ㄕㄥ ㄓˊ ㄕㄨˋ

луаньшэн чжишу

/lu̯än³⁵ ʂɤŋ⁵⁵ ʈ͡ʂʐ̩⁵¹⁻⁵³ ʂu⁵¹/

/lu̯än³⁵ ʂɤŋ⁵⁵ ʈ͡ʂʐ̩³⁵ ʂu⁵¹/

/lu̯än³⁵ ʂɤŋ⁵⁵ ʈ͡ʂʐ̩⁵¹⁻⁵³ ʂu⁵¹/

/lu̯än³⁵ ʂɤŋ⁵⁵ ʈ͡ʂʐ̩³⁵ ʂu⁵¹/


孿生素數

ㄌㄨㄢˊ ㄕㄥ ㄙㄨˋ ㄕㄨˋ

луаньшэн сушу

/lu̯än³⁵ ʂɤŋ⁵⁵ su⁵¹⁻⁵³ ʂu⁵¹/

/lu̯än³⁵ ʂɤŋ⁵⁵ su⁵¹⁻⁵³ ʂu⁵¹/


友愛数

ja-noun

友(ゆう)愛(あい)数(すう) • (yūaisū)

(number theory) amicable numbers, two different numbers related in such a way that the sum of the proper divisors of each is equal to the other number.


過剰数

過(か)剰(じょう)数(すう) • (kajōsū)

(number theory) abundant number, a number that is smaller than the sum of its proper divisors


完全数

(number theory) perfect number, a positive integer that is equal to the sum of its positive divisors, excluding the number itself


不足数

(number theory) deficient number, a number for which the sum of proper divisors is less than that number


双子素数

双子素数 (canonical)
futagososū (romanization)

[ɸɯ̟ta̠ɡo̞so̞sɨː]

From 双(ふた)子(ご) (futago) + 素(そ)数(すう) (sosū).

(number theory) twin prime, a prime number that is either 2 less or 2 more than another prime number, such as 3 and 5


中國剩餘定理

ㄓㄨㄥ ㄍㄨㄛˊ ㄕㄥˋ ㄩˊ ㄉㄧㄥˋ ㄌㄧˇ

чжунго шэнъюй динли

/ʈ͡ʂʊŋ⁵⁵ ku̯ɔ³⁵ ʂɤŋ⁵¹ y³⁵ tiŋ⁵¹ li²¹⁴⁻²¹⁽⁴⁾/

/t͡sʊŋ⁵⁵ kʷɔːk̚³ sɪŋ²² jyː²¹ tɪŋ²² lei̯¹³/

Chinese remainder theorem
Chinese remainder theorem

(number theory) Chinese remainder theorem


素數定理

ㄙㄨˋ ㄕㄨˋ ㄉㄧㄥˋ ㄌㄧˇ

/su⁵¹⁻⁵³ ʂu⁵¹⁻⁵³ tiŋ⁵¹ li²¹⁴⁻²¹⁽⁴⁾/

/su⁵¹⁻⁵³ ʂu⁵¹⁻⁵³ tiŋ⁵¹ li²¹⁴⁻²¹⁽⁴⁾/

prime number theorem
prime number theorem


完全數

ㄨㄢˊ ㄑㄩㄢˊ ㄕㄨˋ

/wän³⁵ t͡ɕʰy̯ɛn³⁵ ʂu⁵¹/

/wän³⁵ t͡ɕʰy̯ɛn³⁵ ʂu⁵¹/


p-adic order

(number theory) Of a positive integer n, the exponent of the highest power of p that divides n. Often denoted νₚ(n). For example, ν₂(48)=4.


lifting the exponent

(number theory) A lemma used to calculate the p-adic order of differences and sums of perfect powers.


ecuație diofantică

ro-noun

ecuație diofantică f (plural ecuații diofantice)

Diophantine equation
Diophantine equation


Polignac's conjecture

(number theory) The conjecture that, for any positive even number n, there are infinitely many prime gaps of size n.


Romanov's theorem

(number theory) A theorem stating that, given a fixed base b, the set of numbers that are the sum of a prime and a positive integer power of b has a positive lower asymptotic density.


Dickson's conjecture

Introduced by Leonard Eugene Dickson in 1904.

(number theory) The conjecture that, for a finite set of linear forms a₁ + b₁n, a₂ + b₂n, ..., aₖ + bₖn with bᵢ ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this.


Elliott-Halberstam conjecture

the Elliott-Halberstam conjecture (canonical)

Named for Peter D. T. A. Elliott and Heini Halberstam, who stated the conjecture in 1968.

arithmetic progression
arithmetic progression

(number theory) A conjecture about the distribution of prime numbers in arithmetic progressions, having many applications in sieve theory.


Schinzel's hypothesis H

(number theory) A famous open problem in mathematics, the hypothesis stating that, for every finite collection f_1,f_2,…,f_k of non-constant irreducible polynomials over the integers with positive leading coefficients, one of the following conditions holds: (i) there are infinitely many positive integers n such that all of f_1(n),f_2(n),…,f_k(n) are simultaneously prime numbers, or (ii) there is an integer m>1 (called a fixed divisor) which always divides the product f_1(n)f_2(n)⋯f_k(n).


Fastprimzahl

de-noun

Fastprimzahl f (genitive Fastprimzahl, plural Fastprimzahlen)

Fastprimzahl (genitive)
Fastprimzahlen (plural)
Fastprimzahl (nominative singular)
Fastprimzahlen (definite nominative plural)
Fastprimzahl (genitive singular)
Fastprimzahlen (definite genitive plural)
Fastprimzahl (dative singular)
Fastprimzahlen (dative definite plural)
Fastprimzahl (accusative singular)
Fastprimzahlen (accusative definite plural)


അഭാജ്യസംഖ്യ

head

അഭാജ്യസംഖ്യ • (abhājyasaṅkhya)

ml-noun

അഭാജ്യസംഖ്യ • (abhājyasaṅkhya)

/äːbʱäːd͡ʒjɐsäŋkʰjɐ/

Compare Hindi अभाज्य संख्या (abhājya saṅkhyā).

cognate

अभाज्य संख्या


Szpiro's conjecture

Named for Lucien Szpiro, who formulated it in the 1980s.

(number theory) A conjecture relating to the conductor and the discriminant of an elliptic curve, equivalent in a slightly modified form to the abc conjecture.


Brocard's conjecture

(number theory) The conjecture that there are at least four prime numbers between (pₙ)² and (pₙ₊₁)², where pₙ is the nth prime number, for every n ≥ 2.


歐拉函數

ㄡ ㄌㄚ ㄏㄢˊ ㄕㄨˋ

/ˀoʊ̯⁵⁵ lä⁵⁵ xän³⁵ ʂu⁵¹/

/ˀoʊ̯⁵⁵ lä⁵⁵ xän³⁵ ʂu⁵¹/

Euler's totient function
Euler's totient function

(number theory) Euler's totient function


Wall-Sun-Sun prime

en-noun

Wall-Sun-Sun prime (plural Wall-Sun-Sun primes)

Named after American mathematician Donald Dines Wall and Chinese mathematicians Sun Zhihong and Sun Zhiwei, who have all contributed to the study of such primes.

Wall-Sun-Sun primes are conjectured to exist, but no example has yet been found.

Not a single Wall-Sun-Sun prime 5lt;plt;1.6#92;times 10#123;12#125; exists [McIntosh 1995]. Carry out a search for Wall-Sun-Sun primes somewhere above this limit.

1996, Richard E. Crandall, Topics in Advanced Scientific Computation, Springer, page 113:

Crandall et al. called in [56] such a prime number p satisfying p²#92;vertF#95;#123;p-(#92;fracp 5)#125; a Wall–Sun–Sun prime. There is no known example of a Wall–Sun–Sun prime and the congruence F#95;#123;p-(#92;fracp 5)#125;#92;equiv 0#92;pmod#123;p²#125;, can only be checked through explicit powering computations.

2020, Dorin Andrica, Ovidiu Bagdasar, Recurrent Sequences, Springer, page 88:

(number theory) A (hypothetical) prime number p such that p² divides F_π(p), where F_n is the Fibonacci sequence and π(p) is the pth Pisano period (the period length of the Fibonacci sequence reduced modulo p).

Donald Dines Wall
Sun Zhihong
Sun Zhiwei
Wall–Sun–Sun prime

nombre premier de Wall-Sun-Sun

conjectured prime number of a certain type


rank of apparition

rank of apparition (plural ranks of apparition)

Let (W#95;n) be an EDS^([Elliptic Divisibility Sequence]) associated to an elliptic curve E#47;K and a nonzero point P#92;inE(K) of finite order. Let r#92;ge 2 be the smallest index such that W#95;r#61;0. (The number r is called the rank of apparition of the sequence.)
[…]
Suppose that K is a finite field and that the rank of apparition r of (W#95;n) is at least 4.

1986, Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer, page 114:

1996, D. L. Wells, Residue Counts Modulo Three for the Fibonacci Triangle, G. E. Bergum, Andreas N. Philippou, Alwyn F. Horadam (editors), Applications of Fibonacci Numbers, Kluwer Academic, Softcover reprint, page 535,
A similar identification between Pascal's Triangle modulo p and the Fibonacci Triangle modulo p can be made for primes p which have the length of the period equal to twice their rank of apparition in the Fibonacci Sequence.

Indeed, as shown in [18, Theorem 4.27], there exist sequences #92;#123;U#95;n#92;#125; and primes p for which p has three ranks of apparition. In the previous section, we showed that if p#61;2, then p has no more than two ranks of apparition in #92;#123;U#95;n#92;#125;.

2013, E. L. Roettger, H. C. Williams, R. K. Guy, “Some Extensions of the Lucas Functions”, in Jonathan M. Borwein, Igor Shparlinski, Wadim Zudilin, editors, Number Theory and Related Fields, Springer, page 303:

divisibility sequence
divisibility sequence

(number theory) Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m;

Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m;
such an index for some generalisation of the concept (for example to allow multiple ranks of apparition for a given m).


Cramér's conjecture

Formulated by the Swedish mathematician Harald Cramér in 1936.

(number theory) An estimate for the size of gaps between consecutive prime numbers, stating that p_n+1-p_n=O(( log p_n)²), where pₙ denotes the nth prime number, O is big O notation, and log is the natural logarithm.


Green-Tao theorem

Proved by Ben Green and Terence Tao in 2004.

(number theory) A theorem stating that the sequence of prime numbers contains arbitrarily long arithmetic progressions.


Pólya's conjecture

Posited in 1919 by the Hungarian mathematician George Pólya.

(number theory) The conjecture (disproved in 1958) that at least half of the natural numbers smaller than any given number have an odd number of prime factors.


Hardy-Littlewood circle method

the Hardy-Littlewood circle method (canonical)

Named after G. H. Hardy and J. E. Littlewood, who developed the technique.

(number theory) A method used to compute the residues about zero for the generating function of a series, as part of proving asymptotic behaviour of the series.


Waring's problem

The problem was proposed in 1770 by Edward Waring.

(number theory) The problem of whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers raised to the power k.


magic constant

magic constant (countable and uncountable, plural magic constants)

(mathematics, number theory) The sum of numbers in any row, column, or diagonal of a magic square.


pandiagonal magic square

pandiagonal magic square (plural pandiagonal magic squares)

recreational mathematics
recreational mathematics

(number theory, recreational mathematics) A magic square with the additional property that the broken diagonals also summate to the magic constant.


broken diagonal

broken diagonal (plural broken diagonals)

(mathematics, number theory) In the theory of magic squares, a set of n cells forming two parallel diagonal lines in the square.


most-perfect magic square

most-perfect magic square (plural most-perfect magic squares)

(number theory, recreational mathematics) A magic square of order n containing the numbers 1 to n² and where each 2 × 2 subsquare sums to 2s, where s = n² + 1, and all pairs of integers distant n/2 along a (major) diagonal sum to s.


prime reciprocal magic square

prime reciprocal magic square (plural prime reciprocal magic squares)

(number theory, recreational mathematics) A magic square using the decimal digits of the reciprocal of a prime number.


multimagic square

multimagic square (plural multimagic squares)

(number theory, recreational mathematics) A magic square that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P.


bimagic square

(number theory, mathematics) A magic square that remains magic when all of its numbers are replaced by their squares.


trimagic square

trimagic square (plural trimagic squares)

(number theory, recreational mathematics) A magic square that remains magic when all of its numbers are replaced by their cubes.


Pell number

(mathematics, number theory) An infinite sequence of integers that comprises the denominators of the closest rational approximations to the square root of 2.


équation diophantienne

fr-noun

équation diophantienne f (plural équations diophantiennes)

(number theory) Diophantine equation (polynomial equation whose variables are only permitted to assume integer values)


Dirichlet character

en-noun

Dirichlet character (plural Dirichlet characters)

1) χ(ab)=χ(a)χ(b);

(analytic number theory) A complex-valued arithmetic function χ:ℤ→ℂ that satisfies the following conditions for some positive integer m and all integers a and b:


Gaussian moat

If we can keep finding 'fatter and fatter' Gaussian moats surrounding the origin, then the prime-hiker will have to keep taking longer and longer steps.

2006, Deanna Haunsperger, Stephen Kennedy, The Edge of the Universe: Celebrating Ten Years of Math Horizons, page 49:

The approach we follow is composed by three main components, each one defined by its own algorithm. The first one generates the necessary Gaussian primes, the second one calculates the Gaussian Moat, and the third one calculates the shortest paths.

2020, Hector Florez, Sanjay Misra, Applied Informatics: Third International Conference, ICAI 2020, Ota, Nigeria, October 29–31, 2020, Proceedings, page 483:

The Gaussian moat problem was posed originally by Basil Gordon in 1962 at the International Congress of Mathematicians held in Stockholm, […]

2022, Luca Dal Negro, Waves in Complex Media, page 372:

(number theory) The maximum difference between consecutive numbers in a sequence of distinct Gaussian prime numbers.


facteur premier

fr-noun

facteur premier m (plural facteurs premiers)

décomposition en facteurs premiers


czynnik pierwszy

czynnik pierwszy (nominative singular)
czynniki pierwsze (nominative plural)
czynnika pierwszego (genitive singular)
czynników pierwszych (genitive plural)
czynnikowi pierwszemu (dative singular)
czynnikom pierwszym (dative plural)
czynnik pierwszy (accusative singular)
czynniki pierwsze (accusative plural)
czynnikiem pierwszym (instrumental singular)
czynnikami pierwszymi (instrumental plural)
czynniku pierwszym (locative singular)
czynnikach pierwszych (locative plural)
czynniku pierwszy (singular vocative)
czynniki pierwsze (plural vocative)

rozkładać liczbę na czynniki pierwsze

prime factor
prime factor#English:_Q1137759

(number theory) prime factor (a factor of a given integer which is also a prime number)


Stern-Brocot tree

en-noun

Stern-Brocot tree (plural Stern-Brocot trees)

Introduced independently by Moritz Stern (1858) and Achille Brocot (1861).

(number theory) An infinite complete binary tree whose vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree.


narcissistic number

narcissistic number (plural narcissistic numbers)

(number theory) A number that, in a given base, is the sum of its own digits each raised to the power of the number of digits.


Armstrong number

Armstrong number (plural Armstrong numbers)


Ramanujan's sum

Ramanujan's sum (plural Ramanujan's sums)

Vinogradov's theorem
Vinogradov's theorem

(number theory) A function, usually denoted c_q(n), of two positive integer variables q and n, defined by the formula c_q(n)=∑_(1<a≤q atop (a,q)=1)e^(2πi tfrac aqn),, where (a, q) = 1 means that a only takes on values coprime to q. It is used in the proof of Vinogradov's theorem.


Vinogradov's theorem

Named after Ivan Matveyevich Vinogradov, who proved it in the 1930s.

Goldbach's weak conjecture
Goldbach's weak conjecture

(number theory) A result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers; a weaker form of Goldbach's weak conjecture.


Legendre's conjecture

(number theory) A conjecture stating that there is a prime number between n² and (n+1)² for every positive integer n.


twin prime conjecture

(number theory) A conjecture stating that there are infinitely many twin primes.


Pisano period

Named after Leonardo Bigollo Pisano a.k.a. Fibonacci (c. 1170 – c. 1240–1250).

(number theory) The period (of repetition) of the sequence of Fibonacci numbers reduced modulo a given natural number (≥1); it can be considered to be a function π(n) where n is the modulus of reduction (see modular arithmetic) and the function returns the period (of the reduced Fibonacci sequence) corresponding to that given modulus.


최대공약수

ko-noun

최대공약수 • (choedaegong'yaksu) (hanja 最大公約數)

choedaegong'yaksu (romanization)
最大公約數 (hanja)

[t͡ɕʰø̞dɛɡo̞ŋja̠ks͈u]

[t͡ɕʰø̞de̞ɡo̞ŋja̠ks͈u]

greatest common divisor
greatest common divisor

(arithmetic, number theory) greatest common divisor


chińskie twierdzenie o resztach

chińskie twierdzenie o resztach (nominative singular)
chińskiego twierdzenia o resztach (genitive singular)
chińskiemu twierdzeniu o resztach (dative singular)
chińskie twierdzenie o resztach (accusative singular)
chińskim twierdzeniem o resztach (instrumental singular)
chińskim twierdzeniu o resztach (locative singular)
chińskie twierdzenie o resztach (singular vocative)

Literally, “Chinese theorem about remainders”; see Chinese remainder theorem for more information.

lit

(number theory) the Chinese remainder theorem


최소공배수

choesogongbaesu (romanization)
最小公倍數 (hanja)

[t͡ɕʰwe̞sʰo̞ɡo̞ŋbɛsʰu]

[t͡ɕʰø̞sʰo̞ɡo̞ŋbɛsʰu]

[t͡ɕʰø̞sʰo̞ɡo̞ŋbe̞sʰu]

least common multiple
least common multiple

(arithmetic, number theory) least common multiple


최소공분모

choesogongbunmo (romanization)
最小公分母 (hanja)

[t͡ɕʰø̞sʰo̞ɡo̞ŋbunmo̞]

least common denominator
least common denominator

lowest common denominator
lowest common denominator

(arithmetic, number theory) least common denominator; lowest common denominator


쌍둥이 소수

From 쌍(雙)둥이 (ssangdung'i) + 소수(素數) (sosu).


セクシー素数

セクシー素数 (canonical)
sekushīsosū (romanization)

[se̞kɯ̟̊ɕiːso̞sɨː]

(number theory) sexy prime, a prime number that is either 6 less or 6 more than another prime number, such as 5 and 11


いとこ素数

いとこ素数 (canonical)
itokososū (romanization)

(number theory) cousin prime, a prime number that is either 4 less or 4 more than another prime number, such as 3 and 7