Zobrazeno 1 - 10
of 499
pro vyhledávání: '"SURY, B."'
Gerth generalised Cohen-Lenstra heuristics to the prime $p=2$. He conjectured that for any positive integer $m$, the limit $$ \lim_{x \to \infty} \frac{\sum_{0 < D \le X, \atop{ \text{squarefree} }} |{\rm Cl}^2_{\Q(\sqrt{D})}/{\rm Cl}^4_{\Q(\sqrt{D})
Externí odkaz:
http://arxiv.org/abs/2408.11916
We define two variants $e(G)$, $f(G)$ of the Davenport constant $d(G)$ of a finite group $G$, that is not necessarily abelian. These naturally arising constants aid in computing $d(G)$ and are of potential independent interest. We compute the constan
Externí odkaz:
http://arxiv.org/abs/2406.09210
We address three questions posed by Bibak \cite{KB20}, and generalize some results of Bibak, Lehmer and K G Ramanathan on solutions of linear congruences $\sum_{i=1}^k a_i x_i \equiv b \Mod{n}$. In particular, we obtain explicit expressions for the n
Externí odkaz:
http://arxiv.org/abs/2403.01923
In this article, we consider systems of linear congruences in several variables and obtain necessary and sufficient conditions as well as explicit expressions for the number of solutions subject to certain restriction conditions. These results are in
Externí odkaz:
http://arxiv.org/abs/2403.01914
Autor:
Komatsu, Takao, Sury, B.
We prove some polynomial identities from which we deduce congruences modulo $p^2$ for the Fermat quotient $\frac{2^p-2}{p}$ for any odd prime $p$ (Proposition 1 and Theorem 1). These congruences are simpler than the one obtained by Jothilingam in 198
Externí odkaz:
http://arxiv.org/abs/2309.09491
In this note, we use integral binary cubic forms to study the rational cube sum problem. We prove (unconditionally) that for any positive integer $d$, infinitely many primes in each of the residue classes $ 1 \pmod {9d}$ as well as $ -1 \pmod {9d}$,
Externí odkaz:
http://arxiv.org/abs/2301.06970
Autor:
Majumdar, Dipramit, Sury, B.
We show that the Diophantine equation given by X^3+ XYZ = Y^2+Z^2+5 has no integral solution. As a consequence, we show that the family of elliptic curve given by the Weierstrass equations Y^2-kXY = X^3 - (k^2+5) has no integral point.
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Externí odkaz:
http://arxiv.org/abs/2108.02640
Autor:
Majumdar, Dipramit, Sury, B.
Publikováno v:
International Journal of Number Theory 18, No. 9 (2022), 1929-1955
In this article we explicitly describe irreducible trinomials X^3-aX+b which gives all the cyclic cubic extensions of Q. In doing so, we construct all integral points (x,y,z) with GCD(y,z)=1, of the curves X^2+3Y^2 = 4DZ^3 and X^2+27Y^2=4DZ^3 as D va
Externí odkaz:
http://arxiv.org/abs/2107.09013
Autor:
Pradhan, Soham Swadhin, Sury, B.
In this paper, we answer affirmatively a question of H S Sim on representations in characteristic $0$, for a class of metabelian groups. Moreover, we provide examples to point out that the analogous answer is no longer valid if the solvable group has
Externí odkaz:
http://arxiv.org/abs/2106.14278