2

Part of 2012 Federal Competition For Advanced Students, Part 1

Problems(1)

Diophantine equation: n!+An = n^k

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

Determine all solutions

(n, k)

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

n, k \in\mathbb{N}

A = 7

A = 2012

modular arithmeticnumber theorynumber theory proposed