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SMO 2026 Junior Round 1 Question 18

SMO · SMO 2026 Junior Round 1

Question 18

If $a$ and $b$ are positive real numbers such that $\frac1a+\frac1b=\frac1{a-b}$, find the value of $\left\lceil\frac ba\right\rceil$. Here $\lceil x\rceil$ denotes the smallest integer greatest than or equal to $x$. For example, $\lceil3.1\rceil=4$.