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MathNet 2001 — Part 01 Question 32

Math Olympiad Vault · MathNet 2001 — Part 01

Question 32

Find the two smallest natural numbers $n$ such that the fractions
$$
\frac{68}{n+70}, \frac{69}{n+71}, \frac{70}{n+72}, \ldots, \frac{133}{n+135}
$$
are all irreducible.