IMO 1972 Q5 #
Problem: f and g are real-valued functions defined on the real line. For all x and y,
f(x + y) + f(x - y) = 2f(x)g(y). f is not identically zero and |f(x)| ≤ 1 for all x.
Prove that |g(x)| ≤ 1 for all x.
mathlib-archive / imo.imo1972_q5
Problem: f and g are real-valued functions defined on the real line. For all x and y,
f(x + y) + f(x - y) = 2f(x)g(y). f is not identically zero and |f(x)| ≤ 1 for all x.
Prove that |g(x)| ≤ 1 for all x.