Hostname: page-component-6bf8c574d5-2jptb Total loading time: 0 Render date: 2025-03-03T03:39:28.984Z Has data issue: false hasContentIssue false
  • English
  • Français

The Equation Xk + Yk = Zk In Commuting Rational Matrices

Published online by Cambridge University Press:  20 November 2018

David E. Rush
David E. Rush*
Affiliation:
University of CaliforniaRiverside, California 92521
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Solutions of Xk + Yk = Zk in invertible pairwise commuting rational 2 × 2 matrices are determined for k = 3, 4, 6, 9, from the analogous results of A. Aigner for algebraic number fields.

Keywords

10M2015A3612A2510J06
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 4 , 01 December 1983 , pp. 406 - 409
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Aigner, A., Über die Möglichkeit von X4+Y4 = Z4 in quadratischen Körpern, Jahresber, d. Deutschen Math. Verein. 43 (1934), 226-229.Google Scholar
2. Aigner, A., Die Unmöglichkeit von X6 + y6 = Z6 and X9+y9 = Z9 in quadratischen Korpern, Monatsh. F. Math., 61 (1957), 147-150.Google Scholar
3. Barnett, I. A. and Weitkamp, H. M., The equation Xn + Yn+Zn = 0 in rational binary matrices. An. Str. Univ. “Al, I. Cuza”, Sect. 1, (NS) 7 (1961), 1–64.Google Scholar
4. Bolker, E. D., Solutions of Ak + Bk = Ck in n x n integral matrices, Amer. Math. Monthly, 75 (1968), 759-760.Google Scholar
5. Brenner, J. L. and J. de Pillis, , Fermafs equation Ap + BpP = Cp for matrices of integers, Math. Mag., 45 (1972), 12-15.Google Scholar
6. Cullen, C. G., Matrices and Linear Transformations, Addison-Wesley, Reading, Mass. 1972.Google Scholar
7. Domiaty, R. Z., Solutions of X4+ Y4 = Z4 in 2 × 2 integral matrices, Amer. Math. Monthly, 73 (1966), p. 631.Google Scholar
8. Fogels, E., Über die Möglichkeit einiger diophantischer Gleichung 3 and 4 Grades in quadratischen Körpern. Comm. Math. Helv. 10 (1938), 263-269.Google Scholar
9. Gibson, P. M., Solutions of Ak+Bk = Ckin nonsingular integral matrices, Math. Mag. 43 (1970), 275-276.Google Scholar
10. Jacobson, N., Lectures in Abstract Algebra, vol II, Van Nostrand Reinhold, New York, 1953.Google Scholar
11. Ribenboim, P., 13 Lectures on Fermafs Last Theorem, Springer-Verlag, New York. Heidelberg-Berlin, 1979.Google Scholar