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A Class of Soluble Diophantine Equations

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:14 Nov 2014 19:19

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