Glasnik matematički, Vol. 47 No. 1, 2012.
Original scientific paper
https://doi.org/10.3336/gm.47.1.04
A note on the simultaneous Pell equations x^2-ay^2=1 and z^2-by^2=1
Maohua Le
; Department of Mathematics, Zhanjiang Normal College, Zhanjiang, Guangdong 524048, P.R. China
Abstract
Let m,n be positive integers with 1 < m < n. Let δ be a positive number with 1/2 < δ < 1 . In this paper we prove that if gcd(m,n)>nδ and n>(8× 1016(log(1016/θ3))3/θ3)1/θ, where θ=min(1-δ, 2δ-1), then the simultaneous Pell equations x2-(m2-1)y2=1 and z2-(n2-1)y2=1 have only one positive integer solution (x,y,z)=(m,1,n).
Keywords
Simultaneous Pell equations; number of solutions
Hrčak ID:
82570
URI
Publication date:
3.6.2012.
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