4

Part of 2010 Benelux

Problems(1)

Quadruples (a,b,p,n) - BxMO 2010

Source:

Find all quadruples

(a, b, p, n)

of positive integers, such that

p

is a prime and a^3 + b^3 = p^n\mbox{.}
(2nd Benelux Mathematical Olympiad 2010, Problem 4)

number theoryBxMOBeneluxDiophantine equation