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
![]() |
PDF
- Published Version
See Usage Policy. 435kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20171120-110513579
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 | ||||||
---|---|---|---|---|---|---|---|
Related URLs: |
| ||||||
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 |
Repository Staff Only: item control page