Published March 1998
| Published
Journal Article
Open
Rationals to and Only to Rationals: 10555
- Creators
- Lagarias, Jeffrey C.
-
Rains, Eric M.
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)?
Additional Information
© 1998 Mathematical Association of America.Attached Files
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- 83341
- Resolver ID
- CaltechAUTHORS:20171120-110513579
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2017-11-20Created from EPrint's datestamp field
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2019-10-03Created from EPrint's last_modified field