The PSLQ procedure can be regarded as a jazzed-up version of an integer-relation algorithm dating back more than 2,000 years to the Greek geometer Euclid of Alexandria (365–300 B.C.). The Euclidean ...

A vector $m = (m_1,\ldots, m_n) \in \mathbf{Z}^n\backslash\{0\}$ is called an integer relation for the real numbers $\alpha_1,\ldots, \alpha_n$, if $\sum \alpha_im_i ...

This is a preview. Log in through your library . Abstract Let $x = (x_1, x_2,\ldots, x_n)$ be a vector of real numbers. $x$ is said to possess an integer relation if ...

The global optimization of integer and mixed integer non-linear problems has a lot of applications in engineering. In this paper a heuristic algorithm is developed using line-up competition and ...

Abstract: The problem of Integer Factorization deals with the disintegration of an integer into prime factors. This has direct applications in cryptanalysis, particularly in breaking the RSA. Lately, ...

Abstract: As is well known that the security of RSA depends on the hardness of integer factorization. The integer factorization method ToolBox includes many algorithms: trial division algorithm, ...