[PDF] Top 20 Gauss' algorithm for the solution of quadratic diophantine equations
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Gauss' algorithm for the solution of quadratic diophantine equations
... The nunber of reduced forms in a period of rJuced forms of determinantperiod of the classical continued fractio^ ii lf,"-n.*U"r of terms in the expansion of an appropriate quadratic irra[r] ... See full document
30
On Polynomials Solutions of Quadratic Diophantine Equations
... Pell equations is to determine whether non-trivial solutions exist or ...non-trivial solution, all solutions are obtained as powers of the smallest non-trivial ... See full document
5
On Ternary Quadratic Diophantine Equation
... ternary quadratic Diophantine equations [8-9] has been ...ternary quadratic Diophantine ...ternary quadratic equation 15 x 2 15 y 2 24 xy 438 z 2 and obtain different ... See full document
7
On The Positive Pell Equation $y^2=90 x^2+31$
... binary quadratic Diophantine equations are rich in variety, one may search for the other choices of pell equations and determine their integer solutions along with suitable ... See full document
7
Integral Solutions of an Infinite Elliptic Cone X2 = 4Y2 + 5Z2
... ternary quadratic Diophantine equations are rich in variety, one may search for other choices of Diophantine equations to find their corresponding integer ... See full document
9
On the Negative Pell Equation y2 = 48x2 23
... binary quadratic Diophantine equations (both homogeneous and non-homogeneous) are rich in ...binary quadratic non-homogeneous equations representing hyperbolas respectively are studied ... See full document
8
A Ternary Quadratic Diophantine Equation $x^2+y^2=65z^2$
... ternary quadratic equations are rich in variety, one may search for the other choice of ternary quadratic Diophantine equations and determine their integer solutions along with suitable ... See full document
7
Observations on Ternary Quadratic Diophantine Equation 6(x2+y2) – 11xy+3x+3y+9=72z2
... Ternary quadratic equations are rich in ...ternary quadratic Diophantine equation of the form kxy m ( x y ) z 2 has been studied for non-trivial integral ...ternary quadratic ... See full document
6
On the Hyperbola $2x^2-3y^2=23$
... the Diophantine equation, represented by hyperbola is given by 2 x 2 − 3 y 2 = 23 ...binary quadratic Diophantine equations are rich in variety, one may search for the other choices of ... See full document
9
Integer Solution of the Homogeneous Bi-Quadratic Diophantine Equation with Five Unknowns $(x-y)(x^3-y^3)=(z^2-w^2)p^2$
... Bi-quadratic Diophantine equations, homogeneous and non -homogeneous, have aroused the interest of numerous mathematicians since ambiguity as can be seen from [1-2] particularly In [3-5] ... See full document
7
Observation on the Non-Homogeneous Binary Quadratic Diophantine Equation $5x^2-6y^2=5$
... the Diophantine equation, represented by hyperbola is given by 5 x 2 − 6 y 2 = 5 ...binary quadratic Diophantine equations are rich in variety, one may search for the other choices of ... See full document
8
ON THE TERNARY QUADRATIC DIOPHANTINE EQUATION
... The Diophantine equations offer an unlimited field for research due to their ...for quadratic equations with three ...homogeneous quadratic equation with three unknowns for determining ... See full document
8
Parallel Implementation of the Gauss Seidel Algorithm on k Ary n Cube Machine
... of equations, direct and iterative ...the solution is produced. Gauss elimination and related strategies on a linear sys- tem is an example of such ... See full document
6
The Solution of Yang Mills Equations on the Surface
... H if the norm is sufficiently. Here, we construct a solution on the quadric that is independent of the time. And we also construct a solution of the poly- nomial form. In the process of solving, the ... See full document
10
On the Positive Pell Equation y^2=8x^2+49
... binary quadratic equations of the form y 2 Dx 2 1 where D is non-square positive integer has been selected by various mathematicians for its non-trivial integer solutions when D takes different integral ... See full document
8
Note on the quadratic Gauss sums
... the Gauss and the quadratic Gauss ...the quadratic Gauss sums G(k;p) are equal to the Gauss sums G(k,χ) that correspond to this particular Dirichlet charac- ter ...the ... See full document
7
Iterative solution of quadratic tensor equations for mutual polarisation
... recursion equations that relate the induced dipole moment, linear polarisability, and first hyperpolarisability in the material to the intrinsic values of the same properties of isolated ... See full document
12
Three special systems of double diophantine equations
... solutions. In this context, one may refer (Gopalan et al, 2014; Gopalan et al, 2016; Gopalan et al, 2016; Gopalan et al, 2016; Meena et al, 2016; Gopalan et al, 2016; Devibala et al, 2017). The above results motivated us ... See full document
5
A geometric view of cryptographic equation solving
... GeometricXL algorithm requires us to find a linear combination of a collection of matrices hav- ing rank ...GeometricXL algorithm are of a very particular ...GeometricXL algorithm as described in ... See full document
45
On the Positive Integer Solutions for a Diophantine Equation
... fundamental solution and so is a solution of ...the Diophantine equation in (1) is satisfied for : − 1, that is, ( < + 4) − 42(" < − 3) − 8( < + 4) − 252(" < − 3) − 378 = 0 ... See full document
5
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