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pro vyhledávání: '"Rout, S. S."'
Autor:
N, Darsana, Rout, S. S.
In this paper, we prove two results related to the solutions of norm form equations. Firstly, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations. Next, we give
Externí odkaz:
http://arxiv.org/abs/2410.01688
Autor:
N, Darsana, Rout, S. S.
Let $(U_n)_{n\geq 0}$ be a non-degenerate linear recurrence sequence with order at least two defined over a function field and $\mathcal{O}_S^*$ be the set of $S$-units. In this paper, we use a result of Brownawell and Masser to prove effective resul
Externí odkaz:
http://arxiv.org/abs/2408.09448
Suppose that $(U_{n})_{n \geq 0}$ is a binary recurrence sequence and has a dominant root $\alpha$ with $\alpha>1$ and the discriminant $D$ is square-free. In this paper, we study the Diophantine equation $U_n + U_m = x^q$ in integers $n \geq m \geq
Externí odkaz:
http://arxiv.org/abs/2202.11934
Let $S := \{p_1,\ldots ,p_{\ell}\}$ be a finite set of primes and denote by $\mathcal{U}_S$ the set of all rational integers whose prime factors are all in $S$. Let $(U_n)_{n\geq 0}$ be a non-degenerate linear recurrence sequence with order at least
Externí odkaz:
http://arxiv.org/abs/2104.04808
Autor:
Rout, S. S., Meher, N. K.
Let $S= \{ p_1, \ldots, p_s\}$ be a finite, non-empty set of distinct prime numbers and $(U_{n})_{n \geq 0}$ be a linear recurrence sequence of integers of order $r$. For any positive integer $k,$ we define $(U_j^{(k)})_{j\geq 1}$ an increasing seque
Externí odkaz:
http://arxiv.org/abs/2004.06988
In this paper, we consider the problem about finding out perfect powers in an alternating sum of consecutive cubes. More precisely, we completely solve the Diophantine equation $(x+1)^3 - (x+2)^3 + \cdots - (x + 2d)^3 + (x + 2d + 1)^3 = z^p$, where $
Externí odkaz:
http://arxiv.org/abs/1705.02597
Autor:
Meher, N. K., Rout, S. S.
Let $\{ {U_{n}\}_{n \geq 0} }$ be a non-degenerate binary recurrence sequence with positive discriminant. Let $\{p_1,\ldots, p_s\}$ be fixed prime numbers and $\{b_1,\ldots ,b_s\}$ be fixed non-negative integers. In this paper, we obtain the finitene
Externí odkaz:
http://arxiv.org/abs/1612.05869
Autor:
Mazumdar, Eshita, Rout, S. S.
Let $\{u_{n}\}_{n \geq 0}$ be a non-degenerate binary recurrence sequence with positive, square-free discriminant and $p$ be a fixed prime number. In this paper, we have shown the finiteness result for the solutions of the Diophantine equation $u_{n_
Externí odkaz:
http://arxiv.org/abs/1610.02774
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