OME 1986 Problem 2

A segment $d$ is said to divide a segment $s$ if there is a natural number $n$ such that $s = nd = d+d+ ...+d$ ( $n$ times). (a) Prove that if a segment $d$ divides segments $s$ and $s'$ with $s < s'$ , then it also divides their difference $s'-s$ . (b) Prove that no segment divides the side $s$ and the diagonal $s'$ of a regular pentagon (consider the pentagon formed by the diagonals of the given pentagon without explicitly computing the ratios).