ScienceAsia 39 (2013): 653-655 |doi:
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,c∈OF 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: email@example.com
Received 21 Sep 2012, Accepted 13 Nov 2013