Wolstenholme's theorem revisited (Q6172859)

Wolstenholme's theorem of 1862 states that the numerator of the reduced fraction given by \[ 1+ \frac 12+ \frac 13+ \cdots+ \frac 1{p-1} \] is divisible by \(p^2\) for all prime numbers \(p\geq 5\). This short note is another elementary proof of the theorem that relies entirely on the theory of congruences with no combinatorial arguments.