The first case of Fermat’s last theorem is true for all prime exponents up to 714,591,416,091,389

Granville, Andrew; Monagan, Michael B.

doi:10.1090/S0002-9947-1988-0927694-5

The first case of Fermat’s last theorem is true for all prime exponents up to $714,591,416,091,389$
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Trans. Amer. Math. Soc. 306 (1988), 329-359 Request permission

Abstract:

We show that if the first case of Fermat’s Last Theorem is false for prime exponent $p$ then ${p^2}$ divides ${q^p} - q$ for all primes $q \leqslant 8q$. As a corollary we state the theorem of the title.

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