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A method of solving combinatorial problems by means of an algorithm which is allowed to run forward until a dead end is reached, at which point previous steps are retraced ...

A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem, Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

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

A genetic algorithm is a class of adaptive stochastic optimization algorithms involving search and optimization. Genetic algorithms were first used by Holland (1975). The ...

An algorithm used to recursively construct a set of objects from the smallest possible constituent parts. Given a set of k integers (a_1, a_2, ..., a_k) with a_1<a_2<...<a_k, ...

The Greenfield graph is the name given in this work to the 12-vertex graph illustrated above due to Greenfield (2011). This graph provided the first known example which ...

Given integers a and b with close to 2n bits each, the half-GCD of a and b is a 2×2 matrix [u v; u^' v^'] with determinant equal to -1 or 1 such that ua+vb=r and ...

For n>=1, let u and v be integers with u>v>0 such that the Euclidean algorithm applied to u and v requires exactly n division steps and such that u is as small as possible ...

Neville's algorithm is an interpolation algorithm which proceeds by first fitting a polynomial of degree 0 through the point (x_k,y_k) for k=1, ..., n, i.e., P_k(x)=y_k. A ...