Results 161 to 170 of about 25,597,246 (186)

P-Adic Valuation of the Morgan–Voyce Sequence and p-Regularity

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2017
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Lyes Ait-Amrane
exaly   +3 more sources

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p-adic Valuation of the Sum of Divisors

Frontiers of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Junjia, Chen, Yonggao
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On the p-Adic Valuation of Third Order Linear Recurrence Sequences

Results in Mathematics
In a recent paper, Bilu et al. studied a conjecture of Marques and Lengyel on the $p$-adic valuation of the Tribonacci sequence. In this article, we study the $p$-adic valuation of third order linear recurrence sequences by considering a generalisation of the conjecture of Marques and Lengyel for third order linear recurrence sequences.
Rupam Barman, Deepa Antony
exaly   +3 more sources

p-Adic Valuation of Exponential Sums Associated to Trinomials and Some Consequences

P-Adic Numbers, Ultrametric Analysis, and Applications, 2017
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Francis N Castro
exaly   +3 more sources

The p-adic valuations and degrees of monomial exponential sums

The Ramanujan Journal
In this paper, the authors study the \(p\)-adic valuations and the algebraic degrees of the Gauss sum \(S_k(x^d)\) over \(\mathbb{F}_{p^k}\), which is defined by \begin{align*} S_k(x^d)=\sum_{x\in \mathbb{F}_{p^k}}\zeta_p^{\operatorname{Tr}_k(x^d)}. \end{align*} From the local perspective, one can view the Gauss sum \(S_k(x^d)\) as a \(p\)-adic number.
Yang, Liping, Deng, Xiantao
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p-Adic Valuation of Euler’s Totient Function

Bulletin of the Malaysian Mathematical Sciences Society
Let \(\phi(n)\) be the Euler phi function. The paper proves theorems about what powers of primes can divide \(\phi(n)\) and how large those prime powers can be. Let \(v_p(n)\) be the largest number \(k\) such that \(p^k|n\). Then they note that trivially one has that \(v_2(\phi(n)) \leq \lfloor \log_2 n\rfloor\).
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On sums of powers of the \(p\)-adic valuation of \(n!\)

J. Integer Seq., 2017
Summary: We study sums where the multiplicities of the primes in the prime factorization of \(n\)! appear, and obtain a strong connection between these sums and the Riemann zeta function.
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The \(p\)-adic valuation of Lucasnomials when \(p\) is a special prime

2021
Summary: To determine the \(p\)-adic valuation of a Lucasnomial \(\binom{m}{n}_U\), i.e., of a generalized binomial coefficient with respect to a fundamental Lucas sequence \(U=U(P, Q)\), there is an adequate Kummer rule if \(p\) is a regular prime. No such rule exists if \(p\) is a special prime, i.e., if \(p\) divides \(\operatorname{gcd}(P, Q)\). We
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Matrix Methods of Summation, Regular for p-Adic Valuations

Proceedings of the American Mathematical Society, 1956
Andree, Richard V., Petersen, Gordon M.
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On 3-Adic Valuations of Generalized Harmonic Numbers

Integers, 2012
Ken Kamano
exaly