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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.

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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.

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Additional Information:Copyright © 1951 by the National Academy of Sciences Communicated by E. T. Bell, November 21, 1950
Issue or Number:2
Record Number:CaltechAUTHORS:WARpnas51
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6159
Deposited By: Archive Administrator
Deposited On:27 Nov 2006
Last Modified:02 Oct 2019 23:29

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