Abstract
In this paper we will study the equation for arbitrary integersa ≠ 0,c andb = ±1, ±2 or ±4 Whenb = ±4, we suppose c is divisible by 4. The paper will provide one with a method for finding algorithmically all integral non-trivial solutions of the title equations, where an explicit unit of\(Q(\sqrt {a^2 n^2 - ab} )\) plays an important role.
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