D{é}monstration d'une conjecture de Kruyswijk et Meijer sur le plus petit d{é}nominateur des nombres rationnels d'un intervalle

The average value of the smallest denominator of a rational number belonging to the interval $](j-1)\mathrm{/}N,j\mathrm{/}N]$, 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.