It is well known that the Harmonic numbers
$$H_n=\sum_{k=1}^n \frac{1}{k}$$
are never integers for $n>1$.
Can the difference of two Harmonic numbers
$$H_n-H_m=\sum_{k=m+1}^n \frac{1}{k}$$
be an integer if $n>m>1$?
2026-03-26 21:08:08.1774559288
Can the difference of two Harmonic numbers be an integer?
146 Views Asked by user139000 https://math.techqa.club/user/user139000/detail AtRelated Questions in ELEMENTARY-NUMBER-THEORY
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