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SMO 2007 Open Round 1 Question 5

SMO · SMO 2007 Open Round 1

Question 5

Let $A=\{1,2,\ldots,1000\}$. Let $m$ be the number of two-element subsets $\{a,b\}$ of $A$ such that $ab$ is divisible by $6$. Find $\lfloor m/10\rfloor$. Here $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$.