Problem
ALG-B3-M11-P013 Irrational Coefficient on \(\mathbb Q\)
#13
★★★★★ Level 5 of 5
Prove that there is no additive \(f:\mathbb Q\to\mathbb Q\) such that \(f(f(x))=3x\).
One would need \(c^2=3\).
If \(f(x)=cx\), then \(f(f(x))=c^2x\). We need \(c^2=3\), impossible for rational \(c\). Contradiction.
Contrast with the previous problem.