Compfiles: Catalog Of Math Problems Formalized In Lean

Imo1979P1


import Mathlib.Tactic

/-!
# International Mathematical Olympiad 1979, Problem 1

Suppose that p and q are positive integers such that

  p / q = 1 - 1/2 + 1/3 - 1/4 + ... - 1/1318 + 1/1319.

Prove that p is divisible by 1979.
-/

namespace Imo1979P1

theorem imo1979_p1 (p q : ℤ) (hp : 0 < p) (hq : 0 < q)
    (h : (p : ℚ) / q = ∑ i ∈ Finset.range 1319, (-1 : ℚ)^i / (i + 1)) :
    1979 ∣ p := sorry

File author(s): David Renshaw

This problem has a complete formalized solution.

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