Table of Gaussian integer factorizations information

either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime. The factorizations take the form of an optional unit multiplied...

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition...

method for integers Fermat's factorization method for integers Monoid factorisation Multiplicative partition Table of Gaussian integer factorizations Hardy;...

combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ...

The unique factorization of Euclidean domains is useful in many applications. For example, the unique factorization of the Gaussian integers is convenient...

integers. Its prime elements are known as Gaussian primes. Not every number that is prime among the integers remains prime in the Gaussian integers;...

of "integers" on complex numbers instead of real numbers, like Gaussian integers and Eisenstein integers. If we regard the ring of Gaussian integers,...

theory, an aurifeuillean factorization, named after Léon-François-Antoine Aurifeuille, is factorization of certain integer values of the cyclotomic polynomials...

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus...

the equality of their digit sums with the digit sums of their prime factorizations. Arithmetic dynamics Casting out nines Checksum Digital root Hamming...

Gaussian integers, saying that it is a corollary of the biquadratic law in Z [ i ] , {\displaystyle \mathbb {Z} [i],} but did not provide a proof of either...

the integral definition of the gamma function, resulting in a Gaussian integral. In general, for non-negative integer values of n {\displaystyle n} we...

field of Gaussian rationals and the discriminant is − 4 {\displaystyle -4} . The reason for such a distinction is that the ring of integers of K {\displaystyle...

all entries remain integers if the initial matrix has integer entries Tridiagonal matrix algorithm — simplified form of Gaussian elimination for tridiagonal...

theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that:...

373, 379, 383, 397 (OEIS: A046066) Prime elements of the Gaussian integers; equivalently, primes of the form 4n + 3. 3, 7, 11, 19, 23, 31, 43, 47, 59...

the chosen multiplication algorithm. This table lists the complexity of mathematical operations on integers. On stronger computational models, specifically...

number that is 1 mod 4, the ideal ( p ) {\displaystyle (p)} in the Gaussian integers Z [ i ] {\displaystyle \mathbb {Z} [i]} is a Carmichael ideal. Both...

point-of-view. In particular, Linsker showed that if s {\displaystyle \mathbf {s} } is Gaussian and n {\displaystyle \mathbf {n} } is Gaussian noise with...

ax + by = c Integer factorization: breaking an integer into its prime factors Congruence of squares Dixon's algorithm Fermat's factorization method General...

a Gaussian random polytope. A similar result holds for the number of vertices (of the Gaussian polytope), the number of edges, and in fact, faces of all...

should be chosen as the smallest integer greater than the sum of the input polynomial degrees that is factorizable into small prime factors (e.g. 2,...