7

Part of 2001 JBMO ShortLists

Problems(1)

5-th powers is a no-go - JBMO Shortlist

Source:

Prove that there are are no positive integers

x

y

x^5+y^5+1=(x+2)^5+(y-3)^5

.
[hide="Note"] The restriction

x,y

are positive isn't necessary.

modular arithmeticnumber theory proposednumber theory