A p-adic Study of the Partial Sums of the Harmonic Series
نویسنده
چکیده
This research was supported in part by an operating grant from NSERC. Let Hn = 1 + 1 2 + + 1 n be the n-th partial sum of the harmonic series. A classical result of Wolstenholme states that, if p > 3 is prime, the numerator of Hp 1 is divisible by p2. Here we consider, for a given prime p, the set Jp of n for which p divides the numerator ofHn. This set Jp had been previously determined for p = 2; 3; 5; 7. One of our results is that J11 contains exactly 638 integers, the largest of which is a number of 31 decimal digits. We determine Jp for all p < 550 with three exceptions: 83, 127 and 397.
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ورودعنوان ژورنال:
- Experimental Mathematics
دوره 3 شماره
صفحات -
تاریخ انتشار 1994