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

Abstract

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.