Extensive Study on Integer Factorization With Valuated Binary Tree

Abstract

The paper makes an extensive study on integer factorization with valuated binary tree with on approach that can easily find a node one of whose ancestors contains computable information to factorize an objective odd integer. It proves that an odd composite integer with a divisor of special form can be factorized in relatively short time. Theoretic analyses for the approach are proved with detail mathematical deductions, algorithm is designed to realize the factorization and numerical experiments are made to factorize some Fermat numbers. Experiments show that the computational efficacy is general faster than what were known in the past. The paper once again demonstrates the significance of applying the valuated binary tree on analyzing the odd integers.