On consecutive integers of the form ax², by² and cz²

ArticleOriginal scientific text

Title

Authors ¹

School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.

simultaneous Pell equations, linear forms in logarithms

W. S. Anglin, Simultaneous Pell equations, Math. Comp. 65 (1996), 355-359.
A. Baker and H. Davenport, The equations 3x² - 2 = y² and 8x² - 7 = z², Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.
M. A. Bennett, On the number of solutions of simultaneous Pell equations, J. Reine Angew. Math. 498 (1998), 173-199.
J. H. E. Cohn, The Diophantine equation x⁴ - Dy² = 1, II, Acta Arith. 78 (1997), 401-403.
A. Khintchine, Continued Fractions, 3rd ed., P. Noordhoff, Groningen, 1963.
M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321.
W. Ljunggren, Litt om simultane Pellske ligninger, Norsk Mat. Tidsskr. 23 (1941), 132-138.
W. Ljunggren, Über die Gleichung x⁴ - Dy² = 1, Arch. f. Math. og Naturvidenskab B 45 (1942), 61-70.
D. W. Masser and J. H. Rickert, Simultaneous Pell equations, J. Number Theory 61 (1996), 52-66.
R. G. E. Pinch, Simultaneous Pellian equations, Math. Proc. Cambridge Philos. Soc. 103 (1988), 35-46.
D. T. Walker, On the diophantine equation mX² - nY² = ± 1, Amer. Math. Monthly 74 (1967), 504-513.
P. G. Walsh, On two classes of simultaneous Pell equations with no solutions, Math. Comp., to appear.
P. G. Walsh, On integer solutions to x² - dy² = 1, z² - 2dy² = 1, Acta Arith. 82 (1997), 69-76.