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all triples (p,a,m) satisfying a condition

Source: Bulgarian NMO 2017, 3rd round, p.4

April 21, 2017

algebranumber theory

Problem Statement

Find all triples (p,a,m); p is a prime number,

a,m\in \mathbb{N}

, which satisfy:

a\leq 5p^2

and

(p-1)!+a=p^m

.

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