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We prove a certain polynomial congruence modulo an odd prime p ≥ 5, and as a consequence we obtain a congruence for the cube of the Fermat quotient to base 2 in terms of simple finite sums. This extends known results of a similar nature for the first and second powers of the Fermat quotient.

- Takashi Agoh, Karl Dilcher, Ladislav Skula
- Math. Comput.
- 1998

An analogue for composite moduli m ≥ 2 of the Wilson quotient is studied. Various congruences are derived, and the question of when these quotients are divisible by m is investigated; such an m will be called a “Wilson number”. It is shown that numbers in certain infinite classes cannot be Wilson numbers. Eight new Wilson numbers up to 500 million were… (More)

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