lean_workbook_plus_57141

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Find $f: (0; +\infty) \to \mathbb{R}$ such that \n $f(x)+f(y)=\left (\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}} \right) f(\sqrt{xy}), \forall x,y >0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57141 (x y : ℝ) (f : ℝ → ℝ) (hf: f x + f y = (Real.sqrt (x / y) + Real.sqrt (y / x)) * f (Real.sqrt (x * y))) :  ∃ f: ℝ → ℝ, ∀ x y : ℝ, x > 0 ∧ y > 0 → f x + f y = (Real.sqrt (x / y) + Real.sqrt (y / x)) * f (Real.sqrt (x * y))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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