RELATION BETWEEN TRIANGULAR NUMBERS AND PRIME NUMBERS

摘要

We study a relation between factorials and their additive analog, the triangular numbers. We show that there is a positive integer k such that n! = 2kT where T is a product of triangular numbers. We discuss the primality of T ±1 and the primality of |T ? p| where p is either the smallest prime greater than T or the greatest prime less than T.