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Title of article :
On the number of solutions of binomial Thue inequalities
Author/Authors :
Rلbai، نويسنده , , Zs. and Bennett، نويسنده , , M.A. and Pink، نويسنده , , I.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2013
Pages :
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Abstract :
Let a , b and n be positive integers with n ⩾ 3 and consider the binomial Thue inequality | a x n − b y n | ⩽ 3 . In this paper, we extend a result of the first author and prove that, apart from finitely many explicitly given exceptions, this inequality has at most a single solution in positive integers x and y. In the proof, we combine lower bounds for linear forms in logarithms of algebraic numbers with the hypergeometric method of Thue-Siegel and an assortment of techniques from computational Diophantine approximation.
Keywords :
Thue equations , Diophantine equations
Journal title :
Electronic Notes in Discrete Mathematics
Link To Document :