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June 27th, 2018, 09:18 AM   #1
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Six functions related to FLT

Since Fermat's last theorem has been proved, can it be that with powers greater than 2, the following functions can't all be simultaneously equal to zero with odd powers and all but one of them similarly with even powers? The functions are A^n Mod(B + C), B^n Mod(A - B), C^n Mod (A - B), (B^n +C^n) Mod A, (A^n - C^n) Mod B, (A^n - B^n) Mod C. A B and C being three different non zero integers and A the largest.
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July 9th, 2018, 09:11 AM   #2
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Answer

Somewhat surprisingly, all six are equal to zero when the power is odd and A = B + C, and all but (B^n+C^n) Mod A are zero when the power is any one of form 4n + 2 with A, B and C being any Pythagoras triple. Is this of interest and is it well known?
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