  A classical theorem of Koksma states that for Lebesgue almost every $x>1$ the
sequence $(x^n)_{n=1}^{\infty}$ is uniformly distributed modulo one. In the
present paper we extend Koksma's theorem to the pair correlation setting. More
precisely, we show that for Lebesgue almost every $x>1$ the pair correlations
of the fractional parts of $(x^n)_{n=1}^{\infty}$ are asymptotically
Poissonian. The proof is based on a martingale approximation method.
