ON THE DIOPHANTINE EQUATION 1 + x^sup a^ + z^sup b^ = y^sup n

Several classical problems are related to mixed polynomial-exponential equations. Such equations have been also considered recently by many authors. In the present paper, extending a theorem of the second and last authors, we completely solve the title equation in positive integers a, b, y, n with n...

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Bibliographic Details
Published inJournal of combinatorics and number theory Vol. 8; no. 2; p. 145
Main Authors Bérczes, A, Hajdu, L, Miyazaki, T, Pink, I
Format Journal Article
LanguageEnglish
Published Hauppauge Nova Science Publishers, Inc 01.05.2016
Subjects
Combinatorics
Mathematical problems
Polynomials
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Summary:Several classical problems are related to mixed polynomial-exponential equations. Such equations have been also considered recently by many authors. In the present paper, extending a theorem of the second and last authors, we completely solve the title equation in positive integers a, b, y, n with n ≥ 4 for all values of x, z with 1 ≤ x, z ≤ 50 and x ... z (mod 2). It is interesting to note that apparently deep effective tools (e.g. Baker's method) alone are not sufficient to handle the problem completely. In our arguments we combine local arguments and Baker's method to prove our results.
ISSN:1942-5600