MathDB

The number of integers

Source: ChInese TST 2009 P3

April 4, 2009

modular arithmeticinequalitiesnumber theory proposednumber theory

Problem Statement

Prove that for any odd prime number

p,

the number of positive integer

n

satisfying p|n! \plus{} 1 is less than or equal to

cp^\frac{2}{3}.

where

c

is a constant independent of

p.