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fix: missing positivity condition in erdos_1003.variants.eps87 (#1154)
Statement is false if `x` is negative
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FormalConjectures/ErdosProblems/1003.lean

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@@ -52,7 +52,7 @@ is at most $$\frac{x}{\exp(c(\log x)^{1/3})}$$ for some constant $c > 0$.
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[EPS87] Erd\H os, Paul and Pomerance, Carl and S\'ark\"ozy, Andr\'as, _On locally repeated values of certain arithmetic functions_. {III}. Proc. Amer. Math. Soc. (1987), 1--7.
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-/
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@[category research solved, AMS 11]
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theorem erdos_1003.variants.eps87 (x : ℝ) : ∃ c > 0,
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theorem erdos_1003.variants.eps87 {x : ℝ} (hx : 0 < x) : ∃ c > 0,
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{(n : ℕ) | (n ≤ x) ∧ φ n = φ (n + 1)}.ncard ≤
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x / Real.exp (c * (x.log) ^ (1 / 3)) := by
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sorry

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