Test Contest 1 Problem B

Let $k$ be a nonnegative integer. Let $A = 2 ^ k - 2$ and $B = 2 ^ kA$. Show that $A + 1$ and $B + 1$ have the same set of prime divisors.

import Mathlib.RingTheory.Int.Basic

theorem solution (k : ℕ) (p a b : ℤ) (hp : Prime p) (ha : a = 2 ^ k - 2) (hb : b = 2 ^ k * a) :
    p ∣ (a + 1) ↔ p ∣ (b + 1) := sorry

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