Maths Olympiad Prep

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Number theory Difficulty 5.9 AIME, harder Prove it

16. Prove: The system of indeterminate equations x2+y2=z2,x2y2=w2x^{2}+y^{2}=z^{2}, x^{2}-y^{2}=w^{2} has no positive integer solutions.

Solution

16. Use Theorem 2 to derive a contradiction.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.