Results 1 to 10 of about 366 (35)
Some Results on a Generalized Version of Congruent Numbers
InPrime, 2021 This paper aims to construct a new formula that generates a generalized version of congruent numbers based on a generalized version of Pythagorean triples.
Leomarich F. Casinillo +1 more
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On primitive solutions of the Diophantine equation x2 + y2 = M
Open Mathematics, 2021 We provide explicit formulae for primitive, integral solutions to the Diophantine equation x2+y2=M{x}^{2}+{y}^{2}=M, where MM is a product of powers of Pythagorean primes, i.e., of primes of the form 4n+14n+1. It turns out that this is a nice application
Busenhart Chris +3 more
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Counting certain quadratic partitions of zero modulo a prime number
Open Mathematics, 2021 Consider an odd prime number p≡2(mod3)p\equiv 2\hspace{0.3em}\left(\mathrm{mod}\hspace{0.3em}3). In this paper, the number of certain type of partitions of zero in Z/pZ{\mathbb{Z}}\hspace{-0.1em}\text{/}\hspace{-0.1em}p{\mathbb{Z}} is calculated using a ...
Xiao Wang, Li Aihua
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The extensibility of the Diophantine triple {2, b, c}
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple.
Adžaga Nikola +2 more
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PRIME SOLUTIONS TO POLYNOMIAL EQUATIONS IN MANY VARIABLES AND DIFFERING DEGREES
Forum of Mathematics, Sigma, 2018 Let $\mathbf{f}=(f_{1},\ldots ,f_{R})$ be a system of polynomials with integer coefficients in which the degrees need not all be the same. We provide sufficient conditions for which the system of equations $f_{j}(x_{1},\ldots ,x_{n})=0~(1\leqslant j ...
SHUNTARO YAMAGISHI
doaj +1 more source
A rationality condition for the existence of odd perfect numbers
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 20, Page 1261-1293, 2003., 2003 A rationality condition for the existence of odd perfect numbers is used to derive an upper bound for the density of odd integers such that σ(N) could be equal to 2N, where N belongs to a fixed interval with a lower limit greater than 10300. The rationality of the square root expression consisting of a product of repunits multiplied by twice the base ...
Simon Davis
wiley +1 more source
Counting rational points on smooth cubic surfaces [PDF]
, 2016 We prove that any smooth cubic surface defined over any number field satisfies the lower bound predicted by Manin's conjecture possibly after an extension of small degree.Comment: 11 pages, minor ...
Frei, Christopher, Sofos, Efthymios
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On a class of diophantine equations
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 9, Page 545-553, 2002., 2002 Cohn (1971) has shown that the only solution in positive integers of the equation Y(Y + 1)(Y + 2)(Y + 3) = 2X(X + 1)(X + 2)(X + 3) is X = 4, Y = 5. Using this result, Jeyaratnam (1975) has shown that the equation Y(Y + m)(Y + 2m)(Y + 3m) = 2X(X + m)(X + 2m)(X + 3m) has only four pairs of nontrivial solutions in integers given by X = 4m or −7m, Y = 5m ...
Safwan Akbik
wiley +1 more source
Bounds for the size of sets with the property D(n) [PDF]
, 2003 Let n be a nonzero integer and a_1 < a_2 < ...
Dujella, Andrej
core +6 more sources
Density of solutions to quadratic congruences [PDF]
, 2016 A classical result in number theory is Dirichlet's theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k>1. Building upon a proof by E.M.
Prabhu, Neha
core +2 more sources