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Rationals to and Only to Rationals: 10555

Lagarias, Jeffrey C. and Rains, Eric M. (1998) Rationals to and Only to Rationals: 10555. American Mathematical Monthly, 105 (3). pp. 277-278. ISSN 0002-9890.

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(a) Suppose f(t) ∈ R[t] is a polynomial that maps rationals to rationals and irrationals to irrationals. Show that f(t) = at + b with a and b rational. (b) Does the same conclusion hold under the weaker assumption that f:R → R is an algebraic function (i.e., if there is a polynomial P(x,y) ∈ R[x,y] such that P(t,f(t)) is identically zero)?

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Additional Information:© 1998 Mathematical Association of America.
Subject Keywords:Polynomials, Coefficients, Algebra
Issue or Number:3
Record Number:CaltechAUTHORS:20171120-110513579
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Official Citation:Lagarias, Jeffrey C., et al. “Rationals to and Only to Rationals: 10555.” The American Mathematical Monthly, vol. 105, no. 3, 1998, pp. 277–278. JSTOR,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83341
Deposited By: Tony Diaz
Deposited On:20 Nov 2017 21:55
Last Modified:03 Oct 2019 19:05

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