[PDF] Top 20 On the Ternary Quadratic Diophantine Equation $3(x^2+y^2)-5xy+2(x+y)+4=15z^2$
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On the Ternary Quadratic Diophantine Equation $3(x^2+y^2)-5xy+2(x+y)+4=15z^2$
... L.E.Dickson, History of Theory of Numbers and Diophantine Analysis, Dover Publications, New York 2005.. L.J.Mordell, Diophantine Equations, Academic Press, New York 1970.[r] ... See full document
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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 ... See full document
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On the Non-Homogeneous Ternary Quadratic Equation $2(x^2+y^2)-3xy+(x+y)+1=z^2$
... 2. y ( 2 B − 1 , B ) ( + z 2 B − 1 , B ) − t 26 , B − 11 ≡ 0 ( mod 3 ) ) 3. x ( ) ( ) ( ) A , 1 − y A , 1 + z A , 1 − t 50 , A − 28 ≡ 0 ( mod 3 ) 4. x ( ) ( ) ( ) A , 1 − ... See full document
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Observations on Ternary Quadratic Equation z2 = 82x2 +y2
... the ternary quadratic homogeneous equation k ( x 2 y 2 ) bxy 4 k 2 2 z , (k, ,b 0) has been studied for its non-trivial integral ...the ternary ... See full document
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On the Binary Quadratic Diophantine Equation Y2=272x2+16
... [4] Gopalan.M.A, Sumathi.G, Vidhyalakshmi.S, “Observation on the hyperbola x 2 19 y 2 3 ”, Scholars Journal of the Engineering and Technology 2014;2(2A);152-155. [5] Gopalan.M.A, ... See full document
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On the Homogeneous Ternary Quadratic Equation $11x^2-2y^2 = 9z^2$
... The Diophantine equations offer an unlimited field for research due to their variety ...for quadratic equations with three ...interesting equation 11 x 2 − 2 y 2 = 9 z 2 ... See full document
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Observations on Ternary Quadratic Diophantine Equation 6(x2+y2) – 11xy+3x+3y+9=72z2
... x 2 y 2 ) 11 xy 3 x 3 y 9 72 z 2 (1) The substitution of linear transformations x u v and y u v (2) in (1) leads to, u 3 2 23 v 2 ... See full document
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Integral Solutions of an Infinite Cone α(x^2+y^2 )=(2α 1)xy +(4α 1) z^2
... polynomial equation ( , , … ) = 0, called the Diophantine ...equations. Quadratic Diophantine equations are extremely important in Number ...several Diophantine equations that have no ... See full document
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On The Homogeneous Ternary Quadratic Diophantine Equation 5x2+4y2=189z2
... t 4 , 0 (mod 2 ) y ( , 1 ) 16 Pr 0 (mod 2 ) x ( , ) y ( , ) 9 t 4 , 0 y ( , ) z ( , ) 37 t 4 , 0 z ( 1 , 1 ) S 0 (mod 5 ) ... See full document
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On the Ternary Quadratic Diophantine Equation $3(X^2+Y^2)-5XY=75 Z^2$
... Properties observed are as follows: 1. X ( ) α , 1 − t 16 , α + 77 ≡ 0 ( mod 11 ) 2. 9 Z ( ) ( ) α , 1 + Y α , 1 − t 38 , α ≡ 0 ( mod 23 ) 3. 7 Z ( ) ( ) α , 1 + X α , 1 − t 30 , α ≡ 0 ( mod 51 ) 4. ... See full document
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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 ... See full document
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On the Homogeneous Ternary Quadratic Diophantine Equation 3(X+Y)2 2xy=12z2
... 3 x y xy z is considered and searched for its many different integer solutions. Eight different choices of integer solutions of the above equations are presented. A few interesting relations between the ... See full document
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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 ... See full document
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On the Ternary Quadratic Diophantine Equation 4x2 – 7xy2 + 4y2 + x+y+1=19z2
... The Ternary Quadratic Diophantine equations offer an unlimited field for research by reason of their variety [1, ...another ternary quadratic Diophantine equation 4 ... See full document
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On The Ternary Quadratic Diophantine Equation 4(x2+y2) 3xy=16z2
... The ternary homogeneous quadratic equation given by 4(x 2 y 2 ) 3 xy 16 z 2 representing a cone is analyzed for its non-zero distinct integer ... See full document
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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 ... See full document
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On Homogeneous Cubic Diophantine equation with Four Unknowns $3(x^3+y^3) = 8zp^2$
... cubic equation given by 3 ( x 3 + y 3 ) = 8 zp 2 ...As Diophantine equations are rich in ...cubic equation and determine their corresponding ... See full document
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On the Positive Integer Solutions for a Diophantine Equation
... of Diophantine equation D: M − 42S − 8M − 252S − 378 = 0 ...Keywords: Diophantine equation, polynomial solution, pell’s equation, continued fraction ... See full document
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On the Cubic Diophantine Equation with Four Unknowns $x^2+y^2=z^3-w^3$
... cubic equation with four unknowns given by x 2 + y 2 = z 3 − w 3 ...As Diophantine equations are rich in variety due to their definition, one may attempt to find integer ... See full document
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On Solutions to the Diophantine Equation 3^x + q^y = z^2
... the equation clearly does not ...= 2, 3, 4, and for some particular values when x + y > ...Solutions 3, 5, 7, 12, 13 were already exhibited in ... See full document
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