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Problem 1, Olympic Revenge 2010

Source: IX Olympic Revenge - 2010

January 28, 2013
modular arithmeticnumber theory proposednumber theory

Problem Statement

Prove that the number of ordered triples (x,y,z)(x, y, z) such that (x+y+z)2≡axyzmod  p(x+y+z)^2 \equiv axyz \mod{p}, where gcd(a,p)=1gcd(a, p) = 1 and pp is prime is p2+1p^2 + 1.
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