Is $\frac{(p-1)^p+1}{p^2}$ squarefree for all primes $p \geq 7$? I did some small testing and it seems to hold up to $p \leq 47$. Also, note that the above expression is indeed an integer by binomial expansion.
2026-04-08 12:51:58.1775652718
Is $\frac{(p-1)^p+1}{p^2}$ square-free?
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