Inequality with Prime factorisation(TST problem)

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Fm Jakaria
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Inequality with Prime factorisation(TST problem)

Unread post by Fm Jakaria » Thu Oct 23, 2014 5:45 pm

Let $p$ be a sufficiently large prime. Suppose $(p-1)^p$ has prime factorisation $\prod\limits^n_{i=1} p_i^{e_i}$.
Prove that $\sum p_ie_i \geqslant \frac{p^2}{2}$
You cannot say if I fail to recite-
the umpteenth digit of PI,
Whether I'll live - or
whether I may, drown in tub and die.
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