Ward, Morgan (1951) A Class of Soluble Diophantine Equations. Proceedings of the National Academy of Sciences of the United States of America, 37 (2). pp. 113-114. ISSN 0027-8424 http://resolver.caltech.edu/CaltechAUTHORS:WARpnas51
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Abstract
Let R be a commutative ring with a unit element, F(x) a homogeneous polynomial of degree n in t indeterminates x1, x2, ..., xt with coefficients in R. Let I denote the subring of the coefficients of F(x) in R; that is, the smallest ring containing all of them. We consider the existence of solutions of the diophantine equation F(x) = z^M in R or in I. Here z is an indeterminate and m is a given positive integer.
| Item Type: | Article |
|---|---|
| Additional Information: | Copyright © 1951 by the National Academy of Sciences Communicated by E. T. Bell, November 21, 1950 |
| Record Number: | CaltechAUTHORS:WARpnas51 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:WARpnas51 |
| Alternative URL: | http://www.pnas.org/content/vol37/issue2/ |
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 6159 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Archive Administrator |
| Deposited On: | 27 Nov 2006 |
| Last Modified: | 26 Dec 2012 09:18 |
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