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ScienceAsia 39(2013): 653-655 |doi: 10.2306/scienceasia1513-1874.2013.39.653

On some Diophantine problems in 2×2 integer matrices

Walisa Intrarapak, Supawadee Prugsapitak*

ABSTRACT:     Let F be an algebraic number field with OF its ring of algebraic integers. We find a condition for which the equation aXn+bYn=cZn where a,b,cOF does not hold over a 2×2 matrix ring over a ring of algebraic integers.

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Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hatyai, Songkla 90110 Thailand

* Corresponding author, E-mail: supawadee.p@psu.ac.th

Received 21 Sep 2012, Accepted 13 Nov 2013