Consider.
gcd(N, p) = 1 ⇒ NΦ(p) mod p = 1 by Euler's theorem
gcd(N, p) ≠ 1, N = pb ∙ a, pb ≡ 0 mod p ⇒ NΦ(p) mod p = 0
Hope this helps
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Consider.
gcd(N, p) = 1 ⇒ NΦ(p) mod p = 1 by Euler's theorem
gcd(N, p) ≠ 1, N = pb ∙ a, pb ≡ 0 mod p ⇒ NΦ(p) mod p = 0
Hope this helps