Results 1 to 10 of about 47 (46)
Some Results on a Generalized Version of Congruent Numbers [PDF]
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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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
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
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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
The Manin–Peyre conjecture for smooth spherical Fano varieties of semisimple rank one
Forum of Mathematics, SigmaThe Manin–Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as well as some higher-dimensional smooth spherical Fano varieties.
Valentin Blomer +3 more
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Average Analytic Ranks of Elliptic Curves over Number Fields
Forum of Mathematics, SigmaWe give a conditional bound for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the ...
Tristan Phillips
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Sums of three cubes over a function field
Forum of Mathematics, SigmaWe use a function field version of the circle method to prove that a positive proportion of elements in Fq[t] $\mathbb {F}_q[t]$ double struck upper F Subscript q Baseline left bracket t right bracket are representable as a sum of three cubes of ...
Tim Browning, Jakob Glas, Victor Wang
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