N5

Part of 2014 IMO Shortlist

Problems(1)

IMO Shortlist 2014 N5

Source:

Find all triples

(p, x, y)

consisting of a prime number

p

and two positive integers

x

y

x^{p -1} + y

x + y^ {p -1}

are both powers of

p

.
Proposed by Belgium

IMO Shortlistnumber theoryprimesIMO Shortlist 2014Hi