Abstract
It is proved that the equation (x 2−1)(y 2−1)=(z 2−1)2, |x|≠|y|, |z|≠1, is not solvable in integersx,y,z under the conditionx−y=kz, wherek is a positive integer different from 2.
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References
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Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 181–187, August, 1999.
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Garaev, M.Z., Chubarikov, V.N. Concerning the Sierpinski-Schinzel system of Diophantine equations. Math Notes 66, 142–147 (1999). https://doi.org/10.1007/BF02674869
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DOI: https://doi.org/10.1007/BF02674869