A note on the equation .

Andreescu, Titu

Displaying similar documents to “A note on the equation ${(x + y + z)}^{2} = x y z$ .”

A simple criterion for solvability of both $X^{2} - D Y^{2} = c$ and $x^{2} - D y^{2} = - c$ .

Mollin, R.A. (2001)

The New York Journal of Mathematics [electronic only]

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Corrections to "A quantitative version of Runge's theorem on diophantine equations" (Acta Arith. 62 (1992), 157-172)

P. G. Walsh (1995)

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Solutions of cubic equations in quadratic fields

K. Chakraborty, Manisha V. Kulkarni (1999)

Acta Arithmetica

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Let K be any quadratic field with $_{K}$ its ring of integers. We study the solutions of cubic equations, which represent elliptic curves defined over ℚ, in quadratic fields and prove some interesting results regarding the solutions by using elementary tools. As an application we consider the Diophantine equation r+s+t = rst = 1 in $_{K}$ . This Diophantine equation gives an elliptic curve defined over ℚ with finite Mordell-Weil group. Using our study of the solutions of cubic equations in quadratic...