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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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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by Andrew Granville and Michael B. Monagan
Trans. Amer. Math. Soc. 306 (1988), 329-359
DOI: https://doi.org/10.1090/S0002-9947-1988-0927694-5

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.
References
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Bibliographic Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 306 (1988), 329-359
  • MSC: Primary 11D41
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0927694-5
  • MathSciNet review: 927694