Search

Your search keyword '"Walsh, P. G."' showing total 4 results
Start Over Author "Walsh, P. G." Topic algebra
4 results on '"Walsh, P. G."'

4. A GENERALIZATION OF A THEOREM OF BUMBY ON QUARTIC DIOPHANTINE EQUATIONS.

Author

BENNETT, MICHAEL A., TOGBÉ, ALAIN, and WALSH, P. G.

Subjects
PELL'S equation, ELLIPTIC curves, HYPERGEOMETRIC functions, DIOPHANTINE equations, ALGEBRA
Abstract

Bumby proved that the only positive integer solutions to the quartic Diophantine equation 3X4 - 2Y2 = 1 are (X, Y) = (1, 1),(3, 11). In this paper, we use Thue's hypergeometric method to prove that, for each integer m ≥ 1, the only positive integers solutions to the Diophantine equation (m2 + m + 1)X4 - (m2 + m)Y2 = 1 are (X,Y) = (1, 1),(2m + 1, 4m2 + 4m + 3). [ABSTRACT FROM AUTHOR]

Published
2006
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results