Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Hemar Godinho"'
Publikováno v:
Publicationes Mathematicae Debrecen. 101:63-101
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4dfdbe2f25e91b50fec1fcf58f9b0c01
https://doi.org/10.5486/pmd.2022.9146
https://doi.org/10.5486/pmd.2022.9146
Autor:
Hemar Godinho, Victor G. L. Neumann
Publikováno v:
International Journal of Number Theory. 17:2113-2130
In this paper, we consider the Diophantine equation in the title, where [Formula: see text] are distinct odd prime numbers and [Formula: see text] are natural numbers. We present many results given conditions for the existence of integers solutions f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::723a058f0d63067c929d307b596d0ee9
https://doi.org/10.1142/s1793042121500792
https://doi.org/10.1142/s1793042121500792
Publikováno v:
The Ramanujan Journal. 55:297-307
In this paper we present a new formula for the number of unrestricted partitions of n. We do this by introducing a correspondence between the number of unrestrited partitions of n and the number of non-negative solutions of systems of two equations,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c9073ed77498bc118820c7460df882d2
https://doi.org/10.1007/s11139-019-00211-7
https://doi.org/10.1007/s11139-019-00211-7
Autor:
Hemar Godinho, Michael P. Knapp
Publikováno v:
Michigan Math. J. 69, iss. 3 (2020), 533-543
For any positive integer $k$ , we define $\Gamma ^{*}(k)$ to be the smallest number $s$ such that every diagonal form $a_{1}x_{1}^{k}+a_{2}x_{2}^{k}+\cdots +a_{s}x_{s}^{k}$ in $s$ variables with integer coefficients must have a nontrivial zero in eve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a113fded88750f9d4a02a56627a7d31
https://projecteuclid.org/euclid.mmj/1596700817
https://projecteuclid.org/euclid.mmj/1596700817
Autor:
Luciana Ventura, Hemar Godinho
Publikováno v:
Journal of Number Theory. 177:211-247
One version of Artin's Conjecture states that for a pair of diagonal forms of degree k, with integer coefficients, there exist nontrivial common p-adic zeros provided the number of variables is greater than 2 k 2 . This version of the conjecture is k
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c5ac7f1296ff2b66083501329503ad25
https://doi.org/10.1016/j.jnt.2017.01.005
https://doi.org/10.1016/j.jnt.2017.01.005
Publikováno v:
Mathematica Slovaca. 66:565-574
In this paper, we find all solutions of the Diophantine equation x2 + C= y n in integers x, y ≥ 1, a, b, c ≥ 0, n ≥ 3, with gcd(x, y) = 1, when C= 2 a 3 b 17 c and C = 2 a 13 b 17 c .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::10768a3e57f77b75dc8db88f99d60247
https://doi.org/10.1515/ms-2015-0159
https://doi.org/10.1515/ms-2015-0159
Let [Formula: see text] be a finite abelian group of exponent [Formula: see text], written additively, and let [Formula: see text] be a subset of [Formula: see text]. The constant [Formula: see text] is defined as the smallest integer [Formula: see t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9c8305997d4f5151888089a7fc56fe79
http://arxiv.org/abs/1810.13021
http://arxiv.org/abs/1810.13021
Publikováno v:
Acta Mathematica Hungarica. 143:249-268
Let \(a\in \mathbb {N}\). We discuss the diophantine equation $$v(v+1)=u(u+a)(u+2a) $$ and some important arithmetic properties of the associated cubic field. We also present a detailed account of the cases a=2 and a=5.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::634ec127e04fca575eeb84ba19b52f5a
https://doi.org/10.1007/s10474-013-0374-0
https://doi.org/10.1007/s10474-013-0374-0
Publikováno v:
Journal of Number Theory. 133:176-194
A special case of a conjecture attributed to Artin states that any system of two homogeneous diagonal forms of degree k with integer coefficients should have nontrivial zeros over any p-adic field Q p provided only that the number of variables is at
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e24b0181489342b8ed18c9f9a5bf1211
https://doi.org/10.1016/j.jnt.2012.06.004
https://doi.org/10.1016/j.jnt.2012.06.004
Publikováno v:
Acta Arithmetica. 132:393-399
(∗) a11X k 1 + · · ·+ a1NX N = 0, .. .. .. aR1X k 1 + · · ·+ aRNX N = 0 with coefficients aij in O. Write the degree as k = pτm with p m. A solution x = (x1, . . . , xN ) ∈ KN is called non-trivial if at least one xj is non-zero. It is a s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2dc50316fbfd34a0a931a9a0b64b3f4d
https://doi.org/10.4064/aa132-4-8
https://doi.org/10.4064/aa132-4-8