Diophantine equations with Bernoulli polynomials
Solutions of cubic equations in quadratic fields
Let K be any quadratic field with 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 . 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 fields...
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