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MathNet 2023-part-06 — 191 problems (EN–VI) Question 77

Math Olympiad Vault · MathNet 2023-part-06 — 191 problems (EN–VI)

Question 77

Determine all triples $(a, b, p)$ of positive integers where $p$ is prime and the equation
$$
(a+b)^{p} = p^{a} + p^{b}
$$
is satisfied.