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Home » \( k \) is divisible by the sum of its digits. - inBeat

\( k \) is divisible by the sum of its digits. - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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Question: For all real numbers $ a, b, c $, find the number of functio...
for all $ a, b, c \in \mathbb{R} $.
f(a + b + c) = f(a) + f(b) + f(c) \quad \forall a, b, c \in \mathbb{R}
Let’s set $ a = b = c = 0 $:
f(0) = 3f(0) \Rightarrow 2f(0) = 0 \Rightarrow f(0) = 0
Now, set $ c = 0 $:
This is the **Cauchy Functional Equation**, whose solutions over $ \ma...
Under the Axiom of Choice, there are **infinitely many** additive func...
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