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Old 2019-10-21, 20:03   #9
Dr Sardonicus
 
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Feb 2017
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Your first argument, beginning "Let it be initially assumed that A and B have a highest common factor = 1..." does not use the condition that x > 2 and y > 2. Therefore, if your argument were valid, it would follow that A^2 + B^2 = C^n had no solutions with n > 2 odd.

However, 2^2 + 11^2 = 5^3.

This is a counterexample to your purported proof, but not to Beal's conjecture.
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