1967 AMC 12 Question 25
AMC12 · 1967 AMC 12
For every odd number $p\gt1$ we have:
$(p-1)^{\frac{p-1}{2}}-1$ is divisible by
$p-2$
$(p-1)^{\frac{p-1}{2}}+1$ is divisible by $p$
$(p-1)^{\frac{p-1}{2}}$ is divisible by $p$
$(p-1)^{\frac{p-1}{2}}+1$ is divisible by $p+1$
$(p-1)^{\frac{p-1}{2}}-1$ is divisible by $p-1$