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Solving a functional equation using Lean

February 22, 2021

Here is a problem from the 2019 Brazil Undergrad MO:

Find all functions \(f: \mathbb{R} \rightarrow \mathbb{R}\) satisfying \(f(x f(y) + f(x)) + f(y^2) = f(x) + y f(x + y)\)

I was curious to see if I could formalize and prove/verify this in Lean, so here goes.

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