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. https://resolver.caltech.edu/CaltechAUTHORS:20171120-110513579
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Abstract
(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)?
| Item Type: | Article | ||||||
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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 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171120-110513579 | ||||||
| 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, www.jstor.org/stable/2589100 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 83341 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 20 Nov 2017 21:55 | ||||||
| Last Modified: | 03 Oct 2019 19:05 |
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