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An extension of Boyd's $p$-adic algorithm for the harmonic serie | | Mathew D. Roger
; | | Date: |
17 Aug 2007 | | Abstract: | In this paper we will extend a $p$-adic algorithm of Boyd in order to study
the size of the set: [J_p(y)=left{n :sum_{j=1}^{n}frac{y^j}{j}equiv
0(mod p)
ight}.] Suppose that $p$ is one of the first 100 odd primes and
$yin{1,2,...,p-1}$, then our calculations prove that $|J_p(y)|<infty$ in
24240 out of 24578 possible cases. Among other results we show that
$|J_{13}(9)|=18763$. The paper concludes by discussing some possible
applications of our method to sums involving Fibonacci numbers. | | Source: | arXiv, 0708.2439 | | Services: | Forum | Review | PDF | Favorites | |
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