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Show that for an odd integer $n ≥ 5$, $5^{n-1}\binom{n}{0}-5^{n-2}\binom{n}{1}+…+\binom{n}{n-1}$ is not a prime number.
I would prefer no total solutions and just a hint as to whether or not I’m at a dead end with my solution method.
So far this is my work:
From the binomial expansion,
$$\sum_{j=0}^n 5^{n-j}(-1)^j\...
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