Strong pseudoprimes, covering systems of congruences and generalized bent functions

Abstract

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 Kims 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.