Must a continuous function [math]f:\mathbb{R}^n\to \mathbb{R}(n>1)[/math], such that its integral along any straight line is [math]0[/math], be [math]0[/math] everywhere?
How do I prove that when [math]f(x)[/math] is divided by [math]{ x }^{ 3 }-x[/math], the remainder is of the form [math]3r(x)[/math], where [math]r(x)[/math] is a polynomial with integer coefficients and it is given that [math]f(x)[/math] is a polynomial with integer coefficients and [math]f(n)[/math] is divisible by [math]3[/math] for all integers [math]n[/math]?