If $m$ and $n$ are coprime integers, prove that each of these $m+n-2$ fractions: $$\frac{m+n}{m},\frac{2(m+n)}{m},\frac{3(m+n)}{m},...,\frac{(m-1)(m+n)}{m},$$ $$\frac{m+n}{n},\frac{2(m+n)}{n},\frac{3(m+n)}{n},...,\frac{(n-1)(m+n)}{n}$$ fits one of these open intervals $(1,2),(2,3),(3,4),...,(m+n-2,m+n-1)$

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This doesn't look appropriate for MO. At the very least, it needs motivation. –  Noah S Mar 30 at 23:00
And why these particular tags? –  Aaron Meyerowitz Mar 30 at 23:25