Question

any positive integer p, $p = p2/3 and £p = 9/p, then what is the product of $p and £p?​

Answer 1

Answer:

The most elementary proof I can think of, without explicitly mentioning any number theory: out of the three consecutive numbers p−1, p, p+1, one of them must be divisible by 3; also, since the neighbours of p are consecutive even numbers, one of them must be divisible by 2 and the other by 4, so their product is divisible by 3⋅2⋅4=24 — and of course, we can throw p out since it's prime, and those factors cannot come from it.