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Taking **n = p-1** in (8.4) gives
which implies (1.15) after summing over each ,
applying (8.1) and then using Fermat's Theorem and the Von Staudt--Clausen
Theorem.
With a little more work we see that the left side of (1.15) is
where .
Taking and **n=p-2** in (8.4), and then using a number of the
well--known congruences quoted in section 8 as well as (8.1), we obtain

and .
Substituting these equations into (9.2), and using the fact that
for
, we see that the left side of (1.15) is