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Let p be an arbitrary prime number larger than 4.

Show that (p^2 - 1) is a multiple of 24.

Too difficult or too easy?
Well, here is a slightly tougher one.

Let p be an arbitrary prime number larger than 6.
Let q be given by q = p^4 - 10*(p^2) + 9.
Show that q is a multiple of 1920.