Omni-MATH / Let α be given positive real number, find all the functions f:N^(+)→R such that f(k+m)=f(k)+f(m) holds for any positive integers k, m satisfying αm≤k≤(α+1)m.

Problem

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Let α be given positive real number, find all the functions f:N^(+)→R such that f(k+m)=f(k)+f(m) holds for any positive integers k, m satisfying αm≤k≤(α+1)m.

Let $\alpha$ be given positive real number, find all the functions $f: N^{+} \rightarrow R$ such that $f(k + m) = f(k) + f(m)$ holds for any positive integers $k$, $m$ satisfying $\alpha m \leq k \leq (\alpha + 1)m$.

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Source and history

task_id

f43434a6-57b3-5708-a15a-cbbdeb9d6133

task_key

test--f43434a6-57b3-5708-a15a-cbbdeb9d6133

task_revision_id

4

config / split

/ test

Official source

initial import