BG-MO 2009 Problem 1

The natural numbers $a$ and $b$ satisfy the inequalities $a > b > 1$ . It is also known that the equation $\frac{a^x - 1}{a - 1}=\frac{b^y - 1}{b - 1}$ has at least two solutions in natural numbers, when $x > 1$ and $y > 1$ . Prove that the numbers $a$ and $b$ are coprime (their greatest common divisor is $1$ ).