Let $p>3$ be a prime and let $1+\frac 12 +\frac 13 +\cdots+\frac 1p=\frac ab$.Prove that $p^4$ divides $ap-b$.
Problem
Source: India Postal Coaching 2014 Set 3 Problem 5
Tags: number theory unsolved, number theory
Source: India Postal Coaching 2014 Set 3 Problem 5
Tags: number theory unsolved, number theory
Let $p>3$ be a prime and let $1+\frac 12 +\frac 13 +\cdots+\frac 1p=\frac ab$.Prove that $p^4$ divides $ap-b$.