  In this note we will discuss Euler's solution of the simple difference
equation that he gave in his paper{\it ``De serierum determinatione seu nova
methodus inveniendi terminos generales serierum"} \cite{E189} (E189:``On the
determination of series or a new method of finding the general terms of
series") and also present a derivation for the values of the Riemann
$\zeta$-function at positive integer numbers based on Euler's ideas.
