A time-space tradeoff for Lehman’s deterministic integer factorization method

Fermat’s well-known factorization algorithm is based on finding a representation of natural numbers $N$ as the difference squares. In 1895, Lawrence generalized this idea and applied it to multiples $kN$ original number. A systematic approach choose suitable values for $k$ was introduced by Lehman in 1974, which resulted first deterministic considerably faster than trial division. paper, we construct time-space tradeoff Lawrence’s generalization apply together with Lehman’s result obtain integer runtime complexity $O(N^{2/9+o(1)})$. This exponential improvement since establishment $O(N^{1/4+o(1)})$ bound 1977.