Abstract
The fractional parts of the Bernoulli numbers are dense in the interval $(0,1)$. For every positive integer $k$, the set of all $m$ for which $B_{2m}$ has the same fractional part as $B_{2k}$ has positive asymptotic density.
Citation
Paul Erdős. Samuel S. Wagstaff Jr.. "The fractional parts of the bernoulli numbers." Illinois J. Math. 24 (1) 104 - 112, Spring 1980. https://doi.org/10.1215/ijm/1256047799
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