Special case of Fermat's Theorem

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Luis Gallardo


We prove under a mild condition that the only rationals x, y with x ≥ 0, y≥ 0 and x+y=N(k), for some k ∈ Q*, and xp+yp=1 are x=0, y=1 and x=1, y=0. Here, we let N denote the norm from Q(ωp) to Q for p an odd prime number.


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Gallardo, L. (2022). Special case of Fermat’s Theorem. Gulf Journal of Mathematics, 13(2), 12-18. https://doi.org/10.56947/gjom.v13i2.868