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

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October 30, 2010
modular arithmeticnumber theory proposednumber theory

Problem Statement

Prove that there are are no positive integers xx and yy such that x5+y5+1=(x+2)5+(yāˆ’3)5x^5+y^5+1=(x+2)^5+(y-3)^5.
[hide="Note"] The restriction x,yx,y are positive isn't necessary.
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