强伪素数、覆盖同余式组以及广义bent函数

Strong pseudoprimes, covering systems of congruences and generalized bent functions

本文考虑三个问题:强伪素数的计算、覆盖同余式组和广义bent函数.本文的创新点包括:(1)编程证明3 825 123 056 546 413 051是通过前9个素数为基的Miller-Rabin测试的最小合数;(2)证明Kim的猜想,即任意代数数域上的恰好覆盖同余式组必有模理想重复出现;(3)证明两类广义bent函数不存在.

In this paper, we consider three problems, which are the computation of strong pseudoprimes,covering systems of congruences and generalized bent functions. Our highlights include：（1） through programming,proving that 3 825 123 056 546 413 051 is the smallest composite passing Miller-Rabin test to the first nine prime bases;（2） proving Kim＇s conjecture that exact covering systems of congruences in any algebraic number field must have repeated moduli;（3） proving that two classes of generalized bent functions do not exist.