In 1840 Cauchy [2] 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 [6] succeeded in removing the sign ambiguity in this congruence. In this paper we show how the Davenport-Hasse relation [3] in the form given by Yamamoto [8] can be used to resolve the sign ambiguity in other Cauchy-type congruences. Details are given just for e = 8, 12, and 20.

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Keywords Binomial coefficients (mod p), Davenport-Hasse relation, Sign ambiguities in Cauchy-type congruences
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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