On congruences related to the first case of Fermat's last theorem

Author:
Wells Johnson

Journal:
Math. Comp. **31** (1977), 519-526

MSC:
Primary 10B15; Secondary 10A10

DOI:
https://doi.org/10.1090/S0025-5718-1977-0447108-8

MathSciNet review:
0447108

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Abstract: Solutions to the congruences and are discussed. Congruences of this type arise in the study of the first case of Fermat's Last Theorem. Solutions to these congruences always exist for primes . They are derived from the existence of a primitive cube root of unity . Constructive techniques for finding numerical examples are presented. The results are obtained by examining the *p*-adic expansions of the *p*-adic st roots of unity.

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DOI:
https://doi.org/10.1090/S0025-5718-1977-0447108-8

Keywords:
Congruences,
Fermat's Last Theorem,
*p*-adic roots of unity

Article copyright:
© Copyright 1977
American Mathematical Society