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Home » Question: How many positive 4-digit numbers are divisible by 11? - Abu Waleed Tea

Question: How many positive 4-digit numbers are divisible by 11? - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} = 3 \cdot \frac{(1/3)^2}{1/3} = 3 \cdot \frac{1/9}{1/3} = 3 \cdot \frac{1}{3} = 1

📌 Question: For all real numbers $ a, b, c $, find the number of functions $ f : \mathbb{R} \to \mathbb{R} $ such that

📌 f(a + b + c) = f(a) + f(b) + f(c)

📌 f(ab) = f(a)f(b)

📌 Solution: We are given two functional equations:

📌 $ f(a + b + c) = f(a) + f(b) + f(c) $ for all real $ a, b, c $

📌 $ f(ab) = f(a)f(b) $ for all real $ a, b $

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