quadratic Diophantine equation
A Ternary Quadratic Diophantine Equation $x^2+y^2=65z^2$
... The quadratic Diophantine equation with three unknowns offers an unlimited field for research because of their variety ...for quadratic equations with three ...interesting equation x 2 ...
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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 ...
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On the Ternary Quadratic Diophantine Equation 4x2 – 7xy2 + 4y2 + x+y+1=19z2
... Ternary Quadratic Diophantine equations offer an unlimited field for research by reason of their variety [1, ...ternary quadratic Diophantine equation 4 representing cone for ...
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On the Ternary Quadratic Diophantine Equation $5y^2 = 3x^2+2z^2$
... The Diophantine equations offer an unlimited field for research due to their variety ...for quadratic equations with three ...interesting equation 5 y 2 = 3 x 2 + 2 z 2 representing homogeneous ...
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On The Ternary Quadratic Diophantine Equation 4(x2+y2) 3xy=16z2
... The Diophantine equations offer an unlimited field for research due to their variety [1-3].In particular, one may refer [4-22] for quadratic equations with three unknowns. This communication concerns with ...
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On the Homogeneous Ternary Quadratic Diophantine Equation 3(X+Y)2 2xy=12z2
... In this paper, we have presented infinitely many non-zero distinct integer solutions to the ternary quadratic equation.. As diophantine equation are rich in variety, to conclude, one may[r] ...
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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 ...
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On The Binary Quadratic Diophantine Equation X2 3XY+Y2+18X=0
... In this paper , we have made an attempt to obtain a complete set of non-trivial distinct solutions for the non-homogeneous binary quadratic equation. To conclude , one may search for other choices of ...
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ON THE TERNARY QUADRATIC DIOPHANTINE EQUATION
... The ternary homogeneous quadratic equation given by 3(x 2 y 2 ) 2 xy 4 z 2 representing a cone is analyzed for its non-zero distinct integer solutions. A few interesting relations between the ...
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Observation on the Non-Homogeneous Binary Quadratic Diophantine Equation $5x^2-6y^2=5$
... binary quadratic Diophantine equations of the form ax 2 − by 2 = N , ( a , b , N ≠ 0 ) are rich in variety and have been analyzed by many mathematicians for their respective integer solutions for particular ...
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On the Ternary Quadratic Diophantine Equation $3(X^2+Y^2)-5XY=75 Z^2$
... ternary quadratic equation given by 3 ( X 2 + Y 2 ) − 5 XY = 75 Z 2 is considered and searched for its many different integer ...above equation are ...
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On The Homogeneous Ternary Quadratic Diophantine Equation 5x2+4y2=189z2
... The Diophantine equation offer an unlimited field for research due to their variety 1 3 ...for quadratic equation with three ...interesting equation 5 x 2 4 y 2 189 z 2 ...
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Integral solutions of Quadratic Diophantine equation with five unknowns
... Quadratic equations are rich in variety [1-3].For an extensive review of sizable literature and various problems, one may refer [1-16].. A few interesting relations between the solu[r] ...
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ON THE TERNARY QUADRATIC DIOPHANTINE EQUATION 6z2 = 6x2 - 5y2
... The ternary homogeneous quadratic equation given by 6z 2 6x 2 - 5y 2 representing a cone is analyzed for its non-zero distinct integer solutions. A few interesting relations between the solutions and ...
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On the Binary Quadratic Diophantine Equation Y2=272x2+16
... y representing a hyperbola .A few interesting properties among the solution are presented. Employing the integral solutions of the equation consideration a few patterns of Pythagorean triangles are obtained. ...
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Integral Points on the Ternary Quadratic Diophantine Equation ,
... binary quadratic equation of the form = + 1, where D is non-square positive integer has been studied by various mathematicians for its non-trivial integral solutions when D takes different integral values ...
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Integral Solutions of an Infinite Elliptic Cone X2 = 4Y2 + 5Z2
... ternary quadratic Diophantine equation representing infinite elliptic cone given by = 4 + 5 is analysed for its non-zero distinct integer points on ...
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Integral Solutions of the Diophantine Equation Y2=20x2+4
... binary quadratic Diophantine equation are rich in variety, one may search for the other choices of binary quadratic Diophantine equation and determine their integral solutions ...
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A Study on the Homogeneous Cone x2 + 7y2 = 23z2
... The Ternary Quadratic Diophantine equation representing homogeneous cone under consideration is.. We present below different methods of solving 1.[r] ...
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ON A CLASS OF SOLUTIONS FOR THE HYPERBOLIC DIOPHANTINE EQUATION
... which is not difficult to solve. In the case 2ae − bd 6= 0, by performing the sub- stitutions X = 2ax + by + d and Y = (4ac − 2bd)y + 4af − d 2 , equation (1) reduces to X 2 + Y = 0, which is easy to solve. The ...
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