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MathNet 2014 Question 4

Math Olympiad Vault · MathNet 2014

Question 4

Find all pairs of positive integers $(m, n)$, such that
$$
m + 3n - 5 = 2v - 11d.
$$
Here $v$ is the least common multiple of the numbers $m$ and $n$, and $d$ is the greatest common divisor of $m$ and $n$.