2020 Mathematics Subject Classification: Primary: 11A07 [MSN][ZBL]
Let $p$ be a prime number greater than 3. The numerator of the fraction
is divisible by $p^2$.
An equivalent form of the theorem is that if $x^*$ denotes the solution to the equation $x x^* \equiv 1 \pmod {p^2}$ then
References[edit]
- G. H. Hardy, E. M. Wright,(with R. Heath-Brown, J. Silverman) "An Introduction to the Theory of Numbers" (6th ed.) Oxford University Press (2008) ISBN 0-19-921986-9 Zbl 1159.11001
- N. Rama Rao, "Some congruences modulo $m$" Bull. Calcutta math. Soc. 29 (1938) 167-170 Zbl 64.0097.02
- J. Wolstenholme, "On certain properties of prime numbers", Quart. J. Math. 5 (1862), 35-99