Question 48
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is given such that
$$
f(x+1)+f(x-1)=\sqrt{2}f(x).
$$
Prove that $f$ is a periodic function.
$$
f(x+1)+f(x-1)=\sqrt{2}f(x).
$$
Prove that $f$ is a periodic function.
MathNet 2009-part-03 — 175 problems (EN–VI) Question 48
Math Olympiad Vault · MathNet 2009-part-03 — 175 problems (EN–VI)