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Abstract
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Suppose that P(x), Q(x) in Z[x]
are two relatively prime polynomials, and that P(x) ∕ Q(x) = ∑
n=0∞anxn
has the property that an in Z for all n. We show that if Q(1 ∕ α) = 0, then
α is an algebraic integer. Then, we show that this result can be used to
provide a solution to Problem 11213(b) of the American Mathematical Monthly
(2006).
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Keywords
algebraic number theory, generating functions, secant
function
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Mathematical Subject Classification 2000
Primary: 11R04
Secondary: 11R18
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Milestones
Received: 19 July 2010
Revised: 1 February 2011
Accepted: 2 February 2011
Published: 17 January 2012
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