Diophantine equation
The Diophantine equation ax2+2bxy−4ay2=±1
... 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 a and b are nonnegative integers. The ...
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Solutions of the Diophantine Equation $2^x + p^y = z^2$ When $p$ is Prime
... Abstract. In this article, we consider the Diophantine equation 2 x + p y = z 2 when p = 4N + 3 and p = 4N + 1 are primes. The values x, y, z are positive integers. For each prime, all the possibilities for ...
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A hypothetical upper bound on the heights of the solutions of a Diophantine equation with a finite number of solutions
... a Diophantine equation with a finite number of solutions?, Proceedings of the 2017 Federated Conference on Computer Science and Information Systems ...
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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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All the Solutions of the Diophantine Equation $p^3 + q^2 = z^3$
... the Diophantine equation x n + y n = z n , with integral n > 2, has no solutions in positive integers x, y, ...the equation p 3 + q 3 = z 3 has no solutions in positive integers p, q, ...
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A Ternary Quadratic Diophantine Equation $x^2+y^2=65z^2$
... quadratic Diophantine equation with three unknowns offers an unlimited field for research because of their variety ...interesting equation x 2 + y 2 = 65z 2 representing homogeneous quadratic ...
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Integral Solutions of the Diophantine Equation Y2=20x2+4
... quadratic Diophantine equation are rich in variety, one may search for the other choices of binary quadratic Diophantine equation and determine their integral solutions along with suitable ...
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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 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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Integral solutions of Ternary Cubic Diophantine equation
... In this paper, we have presented three different patterns of non- zero distinct integer solutions of ternary cubic Diophantine equation 8 − 5 = 3 and relations between solutions a[r] ...
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On the Ternary Quadratic Diophantine Equation 4x2 – 7xy2 + 4y2 + x+y+1=19z2
... Diophantine Equation given by 4 represents a cone and is analyzed for its non-zero distinct integer solutions. A few interesting relations among the solutions and special polygonal and pyramided numbers are ...
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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 the Diophantine equation Ax2+22m=yn
... 1. Introduction. Let A,m,n denote positive integers where n is odd > 1 and A square free odd integer. Let K = Q( √ −A), where Q is the field of rational numbers, let further h denote the number of classes of ideals in ...
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On the Positive Integer Solutions for a Diophantine Equation
... the Diophantine equation in (1) is satisfied for : − 1, that is, ( < + 4) − 42(" < − 3) − 8( < + 4) − 252(" < − 3) − 378 = 0 ...this equation is also satisfied for : ...
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On the Diophantine equation x3=dy2±q6
... Using the same argument as in Theorem 2 we can prove the following theorem. Theorem 3 . Let d be a positive integer without prime factor p ≡ 1 (mod 3) and q ≠ 3 an odd prime. If q ±1 (mod 24) and (x, q) = 1, then the ...
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Observations on Ternary Quadratic Diophantine Equation 6(x2+y2) – 11xy+3x+3y+9=72z2
... quadratic Diophantine equation of the form kxy m ( x y ) z 2 has been studied for non-trivial integral ...quadratic diophantine equations have been discussed for its integral ...
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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 ...quadratic Diophantine equations are rich in variety, one may search for the other choices of equations and ...
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On Solutions to the Diophantine Equation $p^x + q^y = z^4$
... of Diophantine equations is very old, very large, and no general method exists to decide whether a given Diophantine equation has any solutions, or how many ...
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On Solutions of the Diophantine Equation $p^x + q^y = z^2$
... Remark 2.3. From Lemma 2.2 it follows that when k = 4 (n = 2), k = 8 (n = 3), and also larger values of k such as k ≥ 16 (n ≥ 4), equation (1) has no solutions. Moreover, from Corollary 2.1 it follows that when k ...
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On the special Diophantine Equation
... quadratic equation of the form y 2 Dx 2 1 where D non-square positive integer has been studied by various mathematician for its non-trivial integral ...quadratic equation y 2 3 x 2 1 ...quartic ...
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