Sciweavers

Share
MOC
1998

On the Diophantine equation |axn - byn | = 1

10 years 4 months ago
On the Diophantine equation |axn - byn | = 1
If a, b and n are positive integers with b ≥ a and n ≥ 3, then the equation of the title possesses at most one solution in positive integers x and y, with the possible exceptions of (a, b, n) satisfying b = a + 1, 2 ≤ a ≤ min{0.3n, 83} and 17 ≤ n ≤ 347. The proof of this result relies on a variety of diophantine approximation techniques including those of rational approximation to hypergeometric functions, the theory of linear forms in logarithms and recent computational methods related to lattice-basis reduction. Additionally, we compare and contrast a number of these last mentioned techniques.
Michael A. Bennett, Benjamin M. M. de Weger
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where MOC
Authors Michael A. Bennett, Benjamin M. M. de Weger
Comments (0)
books