## Compfiles: Catalog Of Math Problems Formalized In Lean

## Imo2004P2

```
import Mathlib.Tactic
/-!
# International Mathematical Olympiad 2004, Problem 2
Find all polynomials P with real coefficients such that
for all reals a,b,c such that ab + bc + ca = 0 we have
P(a - b) + P(b - c) + P(c - a) = 2P(a + b + c).
-/
namespace Imo2004P2
/- determine -/ abbrev SolutionSet : Set (Polynomial ℝ) := sorry
theorem imo2004_p2 (P : Polynomial ℝ) :
P ∈ SolutionSet ↔
∀ a b c, a * b + b * c + c * a = 0 →
P.eval (a - b) + P.eval (b - c) + P.eval (c - a) =
2 * P.eval (a + b + c) := sorry
```

This problem does not yet have a complete formalized solution.

Open with the in-brower editor at live.lean-lang.org: