KöMaL 2007 A437

Let $p$ >3 be a prime and $1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{p} = \frac{a}{b}.$ Prove that $p^4$ divides $ap$ - $b$ .

Official text KöMaL. Quoted with source.

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