View source for Wolstenholme theorem

{{TEX|done}}{{MSC|11A07}}

Let $p$ be a prime number greater than 3.  The numerator of the fraction
$$
\frac{1}{1} + \frac{1}{2} + \cdots + \frac{1}{p-1}
$$
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
$$
1^* + 2^* + \cdots + (p-1)^* \equiv 0 \pmod{p^2} \ .
$$

====References====
* 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