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Volume 10, Issue 2 (2022), Pages [115] - [167]

A NOTE ON THE DIOPHANTINE EQUATION  

[1] Y. Bilu, Y. Bugeaud and M. Mignotte, The Problem of Catalan, Springer, 2014.

 

DOI: https://doi.org/10.1007/978-3-319-10094-4

 

[2] H. Cohen, Number Theory, Springer, New York, 2007.

 

[3] B. Dupuy, A class number criterion for the equation  Acta Arithmetica 127(4) (2007), 391-401.

 

DOI: https://doi.org/10.4064/aa127-4-5

 

[4] B. Dupuy, Note on a determinant, Integers 20 (2020); Article 48.

 

[5] P. Mihailescu, A class number free criterion for Catalan’s conjecture, Journal of Number Theory 99(2) (2003), 225-231.

 

DOI: https://doi.org/10.1016/S0022-314X(02)00101-4

 

[6] P. Mihailescu, New bounds and conditions for the equation of Nagell-Ljunggren, Journal of Number Theory 124(2) (2007), 380-395.

 

DOI: https://doi.org/10.1016/j.jnt.2006.10.010

 

[7] P. Mihailescu, On the class groups of cyclotomic extensions in presence of a solution to Catalan’s equation, Journal of Number Theory 118(1) (2006), 123-144.

 

DOI: https://doi.org/10.1016/j.jnt.2005.08.011

 

[8] P. Ribenboim, Catalan’s Conjecture, Academic, Boston, 1994.

 

[9] L. Washington, Introduction to Cyclotomic Fields, Springer, Berlin, Second Edition, 1997.