Question 35
Find all twice differentiable functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying
$$
f(x)^2 - f(y)^2 = f(x+y) f(x-y)
$$
for all real numbers $x$ and $y$.
$$
f(x)^2 - f(y)^2 = f(x+y) f(x-y)
$$
for all real numbers $x$ and $y$.
MathNet 2016-part-07 — 182 problems (EN–VI) Question 35
Math Olympiad Vault · MathNet 2016-part-07 — 182 problems (EN–VI)