(a) Using Problem 7, show that the exponent of highest power of p dividing (pk − 1)! is [pk −(p−1)k −1]/(p− 1).
[Hint: Recall the identity pk−1=(p− 1 )(pk−1 + ⋯ + p2 + p + 1).]
(b) Determine the highest power of 3 dividing 80! and the highest power of 7 dividing 2400!.
[Hint: 2400 = 74 − 1.]
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