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Prove ax^2+by^2=pz+c has integer solution for p prime

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December 6, 2010
number theory unsolvednumber theory

Problem Statement

If pp is a prime number greater than 22 and a,b,ca, b, c integers not divisible by pp, prove that the equation ax2+by2=pz+cax^2 + by^2 = pz + c has an integer solution.