IMO Shortlist 1997 problem 6


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2. travnja 2012.
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(a) Let n be a positive integer. Prove that there exist distinct positive integers x, y, z such that

x^{n-1} + y^n = z^{n+1}.

(b) Let a, b, c be positive integers such that a and b are relatively prime and c is relatively prime either to a or to b. Prove that there exist infinitely many triples (x, y, z) of distinct positive integers x, y, z such that

x^a + y^b = z^c.
Izvor: Međunarodna matematička olimpijada, shortlist 1997