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MathNet 2017-part-01 — 176 problems (EN–VI) Question 86

Math Olympiad Vault · MathNet 2017-part-01 — 176 problems (EN–VI)

Question 86

How many ordered pairs $(a, b)$, with $a$ and $b$ positive integers, satisfy
$$
a + b + \gcd(a, b) = 33?
$$