show that p^4+p^2−2 is a multiple of 72 for prime p > 3

p^4 + p^2 - 2 = p^4 - 1 + p^2 - 1
= (p^2 - 1)(p^2 + 2)
= (p+1)(p-1)(p^2 + 2)

if p is a prime > 3 then 3 does not devide p so p+1 or p-1 is divisible by 3 and so p^2-1 is divisible by 3
as p^2 + 2 = p^2-1 + 3 so p^2 + 2 is divisible by 3

so (p^2 - 1)(p^2 + 2) is divisible by 9

now as p + 1 and p-1 are 2 consecutive even numbers one of them is divsible by 4 and other by 2 so product is diviisble by 8

so the number is divisible by 72