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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multiplication rules for polynomials


Author: Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 69 (1978), 210-212
MSC: Primary 12D99
MathSciNet review: 0466087
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Abstract: It is proved that the polynomial solutions of the functional equation

$\displaystyle F(z)F( {z + 1/\sqrt a } ) = F( {\sqrt a {z^2} + (b/\sqrt a + 1)z + c/\sqrt a } )$

are precisely $ {(a{z^2} + bz + c)^n}$ if $ {b^2} - 4ac \ne 0$ and $ {(\sqrt a z + b/2\sqrt a )^n}$ if $ {b^2} - 4ac = 0$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0466087-3
PII: S 0002-9939(1978)0466087-3
Keywords: Functional equations, multiplication rules, polynomial factorization
Article copyright: © Copyright 1978 American Mathematical Society