Simultaneous Pell Equations x^2-my^2= 1 and y^2-5z^2 = 1

  • N. A. Sihabudin Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor.Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang,Selangor
  • S. H Sapar Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang,Selangor

Abstract

This paper will discuss the solutions on the simultaneous Pell equations x^2-my^2= 1 and y^2-5z^2 = 1 where ݉ is any positive integer that is not a perfect square and (݉m, 5) = 1. By finding the fundamental solutions of y^2-5z^2 = 1, the possibility of the parity x, y and ݉ will be obtained. Then, the lemmas and theorems will be developed. The solutions to these equations are (2^gs+1,9,4,2^a,k) and (x,y,z,m) = (݉x_i,9,4,2,k_i+1) for certain positive integers a, g, s, k and ݅i ∈ ܰN.


 

Published
2015-12-30
How to Cite
SIHABUDIN, N. A.; SAPAR, S. H. Simultaneous Pell Equations x^2-my^2= 1 and y^2-5z^2 = 1. Menemui Matematik (Discovering Mathematics), [S.l.], v. 37, n. 2, p. 49-53, dec. 2015. ISSN 0126-9003. Available at: <https://myjms.mohe.gov.my/index.php/dismath/article/view/13588>. Date accessed: 10 dec. 2022.

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