The Pell Equation in Quadratic Fields
نویسنده
چکیده
where 7 is a given integer of a quadratic field F, and integral solutions £, 77 are sought in F. It has been shown that equation (1) has an infinite number of solutions if and only if 7 is not totally negative when F is a real field, and 7 is not the square of an integer of F when F is imaginary. We now obtain the following result : Let 7 be such that equation (1) has an infinite number of solutions. If F is a real field it is possible to find a solution £1, rji of (1) so that every solution is given by the equations
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