On the common solution of Pell equations x2-33y2=1 and y2-Dz2=16
By using some elementary methods such as parity analysis,recursive sequence,congruence and properties of Pell e-quation solutions,the common solutions of the equations x2-33y2=1 and y2-Dz2=16 was studied when D=2p1…ps(1 ≤s≤4),where p1,…,ps were different odd prime numbers.In addition to the basic case that D=2×7×151 had a non-trivial solution(x,y,z)=(±48599,±8460,±184),there was only one trivial solution(x,y,z)=(±23,±4,0),thus advancing the study of integer solutions of this kind of Pell equations.
Pell equationcommon solutionodd and even analysisodd prime numbercongruence
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