Shivang's function

Algebra Level 5

Consider the set of all functions \( f:\mathbb{Q} \rightarrow \mathbb{Q} \) such that

\[f(x+f(y))=f(x+y)+f(y) \qquad \forall x, y \in \mathbb{Q}. \]

Find the sum of all possible (distinct) values of \( f(99) \).

This problem is posed by Shivang J.

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