Pairs of Pell Equations Having at Most One Common Solution in Positive Integers
نویسندگان
چکیده
We prove that, for positive integers m and b, the number of simultaneous solutions in positive integers to x2− (4m2−1)y2 = 1, y2−bz2 = 1 is at most one.
منابع مشابه
Solving Families of Simultaneous Pell Equations
possess at most 3 solutions in positive integers (x, y, z). On the other hand, there are infinite families of distinct integers (a, b) for which the above equations have at least 2 positive solutions. For each such family, we prove that there are precisely 2 solutions, with the possible exceptions of finitely many pairs (a, b). Since these families provide essentially the only pairs (a, b) for ...
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Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k − k. In the first section we give some preliminaries from Pell equations x − dy = 1 and x − dy = N , where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x − dy = 1 and x − dy = 2. We give a method for the solutions of these equations. Further we derive recurrence relations...
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تاریخ انتشار 2007