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rename(imo/imo1972_b2 → imo/imo1972_q5): Fix file name (#14037)
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vihdzp committed May 9, 2022
1 parent 8412f1f commit 77c86ba
Showing 1 changed file with 2 additions and 3 deletions.
5 changes: 2 additions & 3 deletions archive/imo/imo1972_b2.lean → archive/imo/imo1972_q5.lean
Expand Up @@ -8,7 +8,7 @@ import data.real.basic
import analysis.normed_space.basic

/-!
# IMO 1972 B2
# IMO 1972 Q5
Problem: `f` and `g` are real-valued functions defined on the real line. For all `x` and `y`,
`f(x + y) + f(x - y) = 2f(x)g(y)`. `f` is not identically zero and `|f(x)| ≤ 1` for all `x`.
Expand All @@ -30,7 +30,6 @@ example (f g : ℝ → ℝ)
(y : ℝ) :
∥g(y)∥ ≤ 1 :=
begin
classical,
set S := set.range (λ x, ∥f x∥),
-- Introduce `k`, the supremum of `f`.
let k : ℝ := Sup (S),
Expand Down Expand Up @@ -86,7 +85,7 @@ begin
end


/-- IMO 1972 B2
/-- IMO 1972 Q5
Problem: `f` and `g` are real-valued functions defined on the real line. For all `x` and `y`,
`f(x + y) + f(x - y) = 2f(x)g(y)`. `f` is not identically zero and `|f(x)| ≤ 1` for all `x`.
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