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...
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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2008
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3255 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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