On the matrix negative Pell equation
Aleksander Grytczuk; Izabela Kurzydło
Discussiones Mathematicae - General Algebra and Applications (2009)
- Volume: 29, Issue: 1, page 35-45
- ISSN: 1509-9415
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] Z. Cao and A. Grytczuk, Fermat's type equations in the set of 2x2 integral matrices, Tsukuba J. Math. 22 (1998), 637-643. Zbl0940.11016
- [2] R.Z. Domiaty, Solutions of x⁴+y⁴=z⁴ in 2x2 integral matrices, Amer. Math. Monthly (1966) 73, 631.
- [3] A. Grytczuk, Fermat's equation in the set of matrices and special functions, Studia Univ. Babes-Bolyai, Mathematica 4 (1997), 49-55 .
- [4] A. Grytczuk, On a conjecture about the equation , Acta Acad. Paed. Agriensis, Sectio Math. 25 (1998), 61-70. Zbl0923.11043
- [5] A. Grytczuk and J. Grytczuk, Ljunggren’s trinomials and matrix equation , Tsukuba J. Math. 2 (2002), 229-235. Zbl1020.11019
- [6] A. Grytczuk and K. Grytczuk, Functional recurences, 115-121 in: Applications of Fibonacci Numbers, Ed. E. Bergum et als, by Kluwer Academic Publishers 1990. Zbl0725.34002
- [7] A. Grytczuk, F. Luca and M. Wójtowicz, The negative Pell equation and Pythagorean triples, Proc. Japan Acad. 76 (2000), 91-94. Zbl0971.11013
- [8] A. Khazanov, Fermat's equation in matrices, Serdica Math. J. 21 (1995), 19-40.
- [9] I. Kurzydło, Explicit form on a GLW criterion for solvability of the negative Pell equation - Submitted.
- [10] M. Le and C. Li, On Fermat's equation in integral 2x2 matrices, Period. Math. Hung. 31 (1995), 219-222. Zbl0849.11035
- [11] Z. Patay and A. Szakacs, On Fermat's problem in matrix rings and groups, Publ. Math. Debrecen 61 (3-4) (2002), 487-494. Zbl1006.11012
- [12] H. Qin, Fermat’s problem and Goldbach problem over , Linear Algebra App., 236 (1996), 131-135.
- [13] P. Ribenboim, 13 Lectures on Fermat's Last Theorem (New York: Springer-Verlag) 1979. Zbl0456.10006
- [14] N. Vaserstein, Non-commutative Number Theory, Contemp. Math. 83 (1989), 445-449.