Cauchy-typec ongruencesf or binomialc oefficients
In 1840 Cauchy  showed that for a prime p = ef +1, e = 20, (10ƒ ƒ)Ξ±(10ƒ 3ƒ)(mod p), and it was not until 1965 that Whiteman  succeeded in removing the sign ambiguity in this congruence. In this paper we show how the Davenport-Hasse relation  in the form given by Yamamoto  can be used to resolve the sign ambiguity in other Cauchy-type congruences. Details are given just for e = 8, 12, and 20.
|Keywords||Binomial coefficients (mod p), Davenport-Hasse relation, Sign ambiguities in Cauchy-type congruences|
|Journal||Proceedings of the American Mathematical Society|
Hudson, R.H. (Richard H.), & Williams, K.S. (1982). Cauchy-typec ongruencesf or binomialc oefficients. Proceedings of the American Mathematical Society, 85(2), 169–174. doi:10.1090/S0002-9939-1982-0652435-9