  The average value of the smallest denominator of a rational number belonging
to the interval $](j-1)/N,j/N]$, where~$j=1,\dots, N$, is proved to be
asymptotically equivalent to~$16\pi^{-2}\sqrt{N}$, when $N$ tends to infinity.
The result had been conjectured in 1977 by Kruyswijk and Meijer.

Number Theory