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Turkey NMO 1999, P-1, find quadruples (x,y,z,w) in (mod 37)

Source:

December 23, 2010

number theory proposednumber theory

Problem Statement

Find the number of ordered quadruples

(x,y,z,w)

of integers with

0\le x,y,z,w\le 36

such that

{{x}^{2}}+{{y}^{2}}\equiv {{z}^{3}}+{{w}^{3}}\text{ (mod 37)}