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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 | ||
-/ | ||
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import Mathlib.Tactic | ||
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import ProblemExtraction | ||
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problem_file | ||
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/-! | ||
# 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. | ||
-/ | ||
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namespace Imo1979P1 | ||
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open scoped BigOperators | ||
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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 |