Numerator of p-1th Harmonic Number is Divisible by Prime p/Proof 2

Proof
From Polynomial x^p - x is Congruent mod p to x to the p-1 Rising:
 * $x^{\overline p} \equiv x^p - x$

Thus from Sum over k of Unsigned Stirling Numbers of First Kind by x^k:
 * $\displaystyle \left[{p \atop k}\right] \equiv \delta_{k p} - \delta _{k 1}$

where:
 * $\displaystyle \left[{p \atop k}\right]$ denotes an unsigned Stirling number of the first kind
 * $\delta$ is the Kronecker delta.

The result follows from Harmonic Number as Unsigned Stirling Number of First Kind over Factorial.