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[Imo1979P1] add problem statement
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dwrensha committed Nov 21, 2023
1 parent 586e6aa commit 59e3c32
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1 change: 1 addition & 0 deletions Compfiles.lean
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@@ -14,6 +14,7 @@ import Compfiles.Imo1964P4
import Compfiles.Imo1968P2
import Compfiles.Imo1968P5
import Compfiles.Imo1974P5
import Compfiles.Imo1979P1
import Compfiles.Imo1981P6
import Compfiles.Imo1982P1
import Compfiles.Imo1986P1
30 changes: 30 additions & 0 deletions Compfiles/Imo1979P1.lean
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/-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/

import Mathlib.Tactic

import ProblemExtraction

problem_file

/-!
# 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

open scoped BigOperators

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

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