There is a problem which i tried a lot but didn't reach to any conclusions:How can i show that the highest power of n which is contained in $(n^r-1)!$ is $\frac{n^r-nr+r-1}{n-1}$?My try:$(n^r-1)!$=$(n^r-1)(n^r-2)(n^r-3)\cdot\cdot\cdot\cdot3.2.1$.But what next can i do?
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