A NOTE ON THE EXPONENTIAL DIOPHANTINE EQUATION X(2)-2(M)=Y(N)

Authors
GUO YD LE MH
Citation
Yd. Guo et Mh. Le, A NOTE ON THE EXPONENTIAL DIOPHANTINE EQUATION X(2)-2(M)=Y(N), Proceedings of the American Mathematical Society, 123(12), 1995, pp. 3627-3629
Citations number
3
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
123
Issue
12
Year of publication
1995
Pages
3627 - 3629
Database
ISI
SICI code
0002-9939(1995)123:12<3627:ANOTED>2.0.ZU;2-Z
Abstract
In this note we prove that the equation x(2) - 2(m) = y(n), x, y, m, n epsilon N, gcd(x, y) = 1, y > 1, n > 2, has only finitely many soluti ons (x, y, m, n). Moreover, all solutions of the equation satisfy 2 da gger mn, n < 2 . 10(9) and max(x, y, m) < C, where C is an effectively computable absolute constant.