# Consecutive Products And Modulos!

Let $$S$$ be the set of all natural numbers $$k$$ such that $$k(k+1) \equiv 60 \pmod{72}$$ and let $$S_{72}$$ be the set of all elements of $$S$$ modulo 72 (so, if $$k \in S$$, then $$a \in S_{72}$$ iff $$a < 72$$ and $$k \equiv a \pmod{72}$$). Find the sum of all elements of $$S_{72}$$.

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