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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

Puni tekst: engleski pdf 102 Kb

str. 53-59

preuzimanja: 305



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).

Ključne riječi

Simultaneous Pell equations, number of solutions

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