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MathNet 2019-part-03 — 184 problems (EN–VI) Question 181

Math Olympiad Vault · MathNet 2019-part-03 — 184 problems (EN–VI)

Question 181

Find all triples $(a, b, c)$ of nonnegative integers that satisfy
$$
a! + 5^{b} = 7^{c}
$$