Quadratic diophantine equations
- 17 November 1960
- journal article
- Published by The Royal Society in Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- Vol. 253 (1026) , 227-254
- https://doi.org/10.1098/rsta.1960.0023
Abstract
Tartakowsky (1929) proved that a positive definite quadratic form, with integral coefficients, in 5 or more variables represents all but at most finitely many of the positive integers not excluded by congruence considerations. Tartakowsky’s argument does not lead to any estimate for a positive integer which, though not so excluded, is not represented by the quadratic form. Here estimates for such an integer are obtained, in terms of the coefficients of the quadratic form. To simplify the argument and improve the estimates, the problem is slightly generalized (by considering a Diophantine equation with linear terms). A combination of analytical and arithmetical methods is needed.Keywords
This publication has 2 references indexed in Scilit:
- On Indefinite Quadratic Forms in Five VariablesProceedings of the London Mathematical Society, 1953
- An Extension of a Problem of KloostermanAmerican Journal of Mathematics, 1946