Bulletin of the Australian Mathematical Society

Research Article

On the exponents modulo 3 in the standard factorisation of n!

Wei Liua1 and Yong-Gao Chena1

a1 Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China, e-mail: ygchen@njnu.edu.cn

Let p be a prime and m be a positive integer. For a positive integer n, let ep(n) be the nonnegative integer with pep(n) | n and pep(n)+1 xs2224 n. As a corollary of our main result we derive an asymptotic formula for the counting function with regard to the condition ep(n!) ≡ xs025B (mod 3), where xs025B xs2208 Z3. In 2001, Sander proved the result with modulus 2.

(Received October 10 2005)