# 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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