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7 x4^n = a^2 + b^2 + c^2 + d^2

Source: Switzerland - 2005 Swiss MO Final Round p7

December 26, 2022
diophantineDiophantine equationnumber theory

Problem Statement

Let n≥1n\ge 1 be a natural number. Determine all positive integer solutions of the equation 7⋅4n=a2+b2+c2+d2.7 \cdot 4^n = a^2 + b^2 + c^2 + d^2.
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