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MathNet 2024-part-03 — 168 problems (EN–VI) Question 158

Math Olympiad Vault · MathNet 2024-part-03 — 168 problems (EN–VI)

Question 158

Find all pairs of prime numbers $(p, q)$ for which there exist positive integers $(m, n)$ such that
$$
(p+q)^m = (p-q)^n.
$$