A Class of Quartic Diophantine Equations with Only Trivial Solutions

T. N. Sinha
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
more » ... numbers can be written as sums of some biquadrates in two different ways with different coefficients.
doi:10.2307/2373840 fatcat:jlb6tro5xbct7oqtkwyr7ewiny