The Diophantine equation $b^2X^4-dY^2=1$
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Publication:4268902
DOI10.1090/S0002-9939-99-05041-8zbMath0980.11021MaRDI QIDQ4268902
Michael A. Bennett, Peter Gareth Walsh
Publication date: 28 October 1999
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
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Powers in recurrence sequences: Pell equations ⋮ Solving the Diophantine equation \(y^2=x(x^2 - n^2)\) ⋮ Complete solutions of the simultaneous Pell equations \((a^2+1)y^2-x^2 = y^2-bz^2 = 1\) ⋮ Integral points on the congruent number curve ⋮ On the \(X\)-coordinates of Pell equations of the form \(px^2\) ⋮ On the solvability of the simultaneous Pell equations x2 − ay2 = 1 and y2 − bz2 = v12 ⋮ On Diophantine equation \(3a^2x^4 - By^2 = 1\) ⋮ A generalization of a theorem of Cohn on the equation \(x^3-Ny^2=\pm 1\) ⋮ A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$ ⋮ Practical solution of the Diophantine equation $y^2 = x(x+2^ap^b)(x-2^ap^b)$ ⋮ The Diophantine equation aX 4 – bY 2 = 1 ⋮ Integral points on the elliptic curve $y^2=x^3-4p^2x$ ⋮ A GENERALIZATION OF A THEOREM OF BUMBY ON QUARTIC DIOPHANTINE EQUATIONS ⋮ INTEGRAL POINTS ON CONGRUENT NUMBER CURVES ⋮ Explicit formula for the solution of simultaneous Pell equations 𝑥²-(𝑎²-1)𝑦²=1, 𝑦²-𝑏𝑧²=1
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