QuestionProve that $n^{7}-n$ is divisible by 42 for all positive integers $n$ and $p>3$ prime, $p^{2} \equiv 1(\bmod 24)$.

Studdy Solution
We can see that both36n^2 and12n are divisible by24. The remaining value is, therefore $p^{2} \equiv (mod\,24)$.
End of Solution. (a) The given expression is divisible by42 for every positive integer. (b) Every prime number not equal to2 or5 divides infinitely many of the numbers $10^n +$.
2. If p>3 is a prime number, then $p^{2} \equiv (mod\,24)$.