Bounds for the least solutions of homogeneous quadratic equations
- 1 April 1955
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 51 (2) , 262-264
- https://doi.org/10.1017/s0305004100030188
Abstract
In this note I obtain bounds for the least integral solutions of the equationin terms ofFor ternary diagonal forms, such bounds have been given by Axel Thue (4) and, more recently, by Holzer (1), Mordell (2) and Skolem (3), but these lead only to bad estimates for general ternaries. So far as I know there have not been given estimates for n≽4. Here I generalize Thue's method to prove:Theorem. Suppose that n ≥ 2 and that f(ɛ) represents zero. Then there is an integral solution of f(a) = 0 withThis publication has 2 references indexed in Scilit:
- On the equation ax2+by2?cz2=0Monatshefte für Mathematik, 1951
- Minimal Solutions of Diophantine EquationsCanadian Journal of Mathematics, 1950