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Diophantine equation: n!+An = n^k

Source: Austrian Federal Competition for Advanced Students 2012, #2

May 23, 2012

modular arithmeticnumber theorynumber theory proposed

Problem Statement

Determine all solutions

(n, k)

of the equation n!+An = n^k with

n, k \in\mathbb{N}

for

A = 7

and for

A = 2012