The Diophantine Equation (D c)
On the Diophantine equation Ax2+22m=yn
... the Diophantine equation Ax 2 = 2 2m = y n , where x and y are ...this equation is due to Nagell [5] who proved that when m = 0,1, this equation has no solutions in integers x and y under the ...
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The Diophantine equation ax2+2bxy−4ay2=±1
... LIONEL BAPOUNGUÉ Received 30 April 2002 We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax 2 + 2bxy − 4ay 2 = ±1, where ...
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On solutions of the Diophantine equation L n + L m = 3 a
... We move our interest on the powers of 3 as a sum of two Lucas numbers. This paper follows the following steps : We first give the generalities on binary linear recurrence, then we demonstrate an important inequality on ...
ON THE DIOPHANTINE EQUATION IN THE FORM THAT A SUM OF CUBES EQUALS A SUM OF QUINTICS
... This equation shows that how sums of some quintics can be written as sums of some ...this Diophantine equation to a quartic or cubic elliptic ...aforementioned equation. We solve the ...
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On Solutions to the Diophantine Equation 3^x + q^y = z^2
... prime, x, y, z are positive integers and x + y = 2, 3, 4. When q > 3, the cases of infinitely many solutions, of a unique solution and of no-solutions are determined. The case q = 3 with particular values x, y is also ...
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On the Diophantine equation x2+2k=yn
... By factorizing the equation z2+ 2 V n, n > 3, k-even, in the field Q(i), various theorems regarding the solutions of this equation in rational integers are proved1. A conjecture regar[r] ...
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On the Diophantine equation x3=dy2±q6
... Now we consider the upper sign in ( 1 ), our main result is laid down in the following.. Theorem 2..[r] ...
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On the Diophantine equation x2+p2k+1=4yn
... It has been proved that if p is an odd prime, y > 1, k ≥ 0, n is an integer greater than or equal to 4, (n,3h) = 1 where h is the class number of the field Q( √ −p), then the equation x 2 + p 2k+1 = 4y n has ...
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The diophantine equation ni+1=k(dn−1)
... Hence, even thomgh each primitive triple generates an infinite family of solutions, no single recurrence relation, as in the case i 4, can describe the family.. THEOREM 3.[r] ...
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Integral Solutions of the Diophantine Equation Y2=20x2+4
... quadratic equation of the form y 2 Dx 2 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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On the Diophantine Equation $p^x + q^y = z^2$
... Abstract. It has been shown in [2] that the title equation has infinitely many solutions when p = 2 and also when p = 3. In this article, it is established and demonstrated for each prime p > 3, that the ...
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On Solutions to the Diophantine Equation $p^x + q^y = z^4$
... title equation has infinitely many ...the equation has exactly one solution in which q is prime, and in all other solutions when p ≥ 2 q is ...the equation has solutions in which q is either prime or ...
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On Solutions of the Diophantine Equation $p^x + q^y = z^2$
... The history of Diophantine Equations dates back to antiquity. There are endless varieties of Diophantine Equations, and there is no general method of solution. It is often asked how big are the gaps between ...
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ON A CLASS OF SOLUTIONS FOR THE HYPERBOLIC DIOPHANTINE EQUATION
... We saw as above that the Diophantine equation D could be transformed into the Diophantine equation ˜ D via the transformation T. Also we showed that x = u + 2µ + 1 and y = v + 3. so we can re ...
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On Polynomial Solutions of Quadratic Diophantine Equation
... variable Diophantine equation have been a subject to extensive research, and their theory constitutes one of the most beautiful, most elaborate part of mathematics, which nevertheless still keeps some of ...
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On the Positive Integer Solutions for a Diophantine Equation
... We saw as above that the Diophantine equation * could be transformed into the Diophantine equation *3 via the transformation ,. Also we showed that ( = + 4 and ) = " − 3 . So we can ...
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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 ...quadratic equation with three ...interesting equation 5 x 2 4 y 2 189 z 2 representing ...
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On the special Diophantine Equation
... Abstract: The binary quadratic equation y 2 7 x 2 9 t , t 0 representing hyperbola is considered for finding its integer solutions. A few interesting properties among the solutions are presented. Also, we ...
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ON THE BINARY QUADRATIC DIOPHANTINE EQUATION
... In [ 7 16 − ] the binary quadratic non- homogeneous equations representing hyperbolas respectively are studied for their non-zero integral solutions.. Also a few interesting properties[r] ...
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On Ternary Quadratic Diophantine Equation
... 1, 2, Department of Mathematics, Cauvery college for women, Trichy Abstract: The ternary quadratic Diophantine equation 15 x 2 15 y 2 24 xy 438 z 2 is analyzed for its non-trivial distinct integral ...
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