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IMO Shortlist 2014 N5

Source:

July 11, 2015

IMO Shortlistnumber theoryprimesIMO Shortlist 2014Hi

Problem Statement

Find all triples

(p, x, y)

consisting of a prime number

p

and two positive integers

x

and

y

such that

x^{p -1} + y

and

x + y^ {p -1}

are both powers of

p

.
Proposed by Belgium