A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
A Class of Quartic Diophantine Equations with Only Trivial Solutions

1978
*
American Journal of Mathematics
*

In this paper, elliptic curves theory is used for solving the quartic Diophantine equation where n ≥ 1, and T i , are rational numbers. We try to transform this quartic to a cubic elliptic curve of positive rank, then get infinitely many integer solutions for the aforementioned Diophantine equation. We solve the above Diophantine equation for some values of n, T i , and obtain infinitely many nontrivial integer solutions for each case. We show among the other things that some numbers can be

doi:10.2307/2373840
fatcat:jlb6tro5xbct7oqtkwyr7ewiny