An extension of Boyd's $p$-adic algorithm for the harmonic series
| dc.creator | Rogers, Mathew D. | |
| dc.date | 2007-08-17 | |
| dc.date.accessioned | 2026-07-07T08:24:14Z | |
| dc.date.available | 2026-07-07T08:24:14Z | |
| dc.description | In this paper we will extend a $p$-adic algorithm of Boyd in order to study the size of the set: \[J_p(y)=\left\{n :\sum_{j=1}^{n}\frac{y^j}{j}\equiv 0(\mod p)\right\}.\] Suppose that $p$ is one of the first 100 odd primes and $y\in\{1,2,...,p-1\}$, 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. | |
| dc.description | 17 pages, 2 tables | |
| dc.identifier | https://arxiv.org/abs/0708.2439 | |
| dc.identifier | http://arxiv.org/abs/0708.2439 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136274 | |
| dc.subject | Number Theory | |
| dc.subject | 11Y99 | |
| dc.title | An extension of Boyd's $p$-adic algorithm for the harmonic series | |
| dc.type | text |