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I was asked to find the greatest common factor of $p^4-1$ for all primes > 5, First I got the value of $7^4 - 1$ which has divisors of $2^4* 3 *5*2$ and $11^4 - 1$ which has divisors $2^4 *3 * 5*61$ which has a GCF of $2^4*3*5$ I can prove that $p^4 - 1$ is divisible by 3 and 5 by casework and 8 by $(p^2+1)(p-1)(p+1)$ are even integers, but I don't know how to prove divisibility of $2^4$, I do not want to bash it since we must check about 7 numbers to prove its divisibility by assigning $16n + x$ where x <16

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