  An $x$-pseudopower to base $g$ is a positive integer which is not a power of
$g$ yet is so modulo $p$ for all primes $p\le x$. We improve an upper bound for
the least such number due to E. Bach, R. Lukes, J. Shallit, and H. C. Williams.
The method is based on a combination of some bounds of exponential sums with
new results about the average behaviour of the multiplicative order of $g$
modulo prime numbers.
