Terminal Lemma

Suppose for any positive integer \(n\), \(s(n)\) is the remainder when \(n\) is divided by \(19\). Find the number of pairs of integers \((a,b)\), such that \(1\leq a\leq b \leq 18,\) and for all \(k=1,2,...,18\) \[k+s(ka)+s(kb)\geq 20\]

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