# A discrete mathematics problem by Jerry Han Jia Tao

Let $$S$$ be a subset of $${0,1,2,\ldots,98}$$ with exactly $$m\geq 3$$ (distinct) elements, such that for any $$x,y\in S$$ there exists $$z\in S$$ satisfying $$x+y \equiv 2z \pmod{99}$$. Find the sum of all possible values of $$m$$.

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