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In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

Given a number n, Fermat's factorization methods look for integers x and y such that n=x^2-y^2. Then n=(x-y)(x+y) (1) and n is factored. A modified form of this observation ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

Elliptic curve primality proving, abbreviated ECPP, is class of algorithms that provide certificates of primality using sophisticated results from the theory of elliptic ...

A conjecture concerning primes.

A Sierpiński number of the second kind is a number k satisfying Sierpiński's composite number theorem, i.e., a Proth number k such that k·2^n+1 is composite for every n>=1. ...

The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their ...

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...