Continuum cardinality of the set of solutions of one class of equations that contain the function of frequency of ternary digits of a number
We study the equation v1 (x) = x, where v1 (x) is the function of frequency of the digit 1 in ternary expansion of x. We prove that this equation has a unique rational solution and a continuum set of irrational solutions. An algorithm for the construction of solutions is proposed. We also describ...
Saved in:
| Date: | 2008 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2008
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3255 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study the equation v1 (x) = x, where v1 (x) is the function of frequency of the digit 1 in ternary expansion of x.
We prove that this equation has a unique rational solution and a continuum set of irrational solutions.
An algorithm for the construction of solutions is proposed. We also describe the topological and metric properties of the set of all solutions.
Some additional facts about equations vi (x), i = 0,2, are also given. |
|---|