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pro vyhledávání: '"Sharma, Vaishavi"'
For fixed integers $D \geq 0$ and $c \geq 3$, we demonstrate how to use $2$-adic valuation trees of sequences to analyze Diophantine equations of the form $x^2+D=2^cy$ and $x^3+D=2^cy$, for $y$ odd. Further, we show for what values $D \in \mathbb{Z}^
Externí odkaz:
http://arxiv.org/abs/2105.03352
Motivated by an expression by Persson and Strang on an integral involving Legendre polynomials, stating that the square of $P_{2n+1}(x)/x$ integrated over $[-1,1]$ is always $2$, we present analog results for Hermite, Chebyshev, Laguerre and Gegenbau
Externí odkaz:
http://arxiv.org/abs/2012.05040
The divisor function $\sigma(n)$ denotes the sum of the divisors of the positive integer $n$. For a prime $p$ and $m \in \mathbb{N}$, the $p$-adic valuation of $m$ is the highest power of $p$ which divides $m$. Formulas for $\nu_{p}(\sigma(n))$ are e
Externí odkaz:
http://arxiv.org/abs/2007.03088
Publikováno v:
In Journal of Number Theory June 2021 223:325-349
Publikováno v:
Hardy-Ramanujan Journal
Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2021, Special Commemorative volume in honour of Srinivasa Ramanujan-2021, 44, pp.116--135
Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2022, Special Commemorative volume in honour of Srinivasa Ramanujan-2021, Volume 44-Special Commemorative volume in honour of Srinivasa Ramanujan-2021, pp.116--135
Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2021, Special Commemorative volume in honour of Srinivasa Ramanujan-2021, 44, pp.116--135
Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2022, Special Commemorative volume in honour of Srinivasa Ramanujan-2021, Volume 44-Special Commemorative volume in honour of Srinivasa Ramanujan-2021, pp.116--135
Motivated by an expression by Persson and Strang on an integral involving Legendre polynomials, stating that the square of $P_{2n+1}(x)/x$ integrated over $[-1,1]$ is always $2$, we present analog results for Hermite, Chebyshev, Laguerre and Gegenbau