Question 1
Find all functions $f:\mathbb R\to\mathbb R$ such that
(i) $\lim_{x\to0}f(x)=f(0)=0$;
(ii) $f(x)f(x^{1959}+x^{54})=f(x^{2013}+x)$ for every real $x$.
(i) $\lim_{x\to0}f(x)=f(0)=0$;
(ii) $f(x)f(x^{1959}+x^{54})=f(x^{2013}+x)$ for every real $x$.