The Representation of Natural Numbers in Terms of Floor Function
Abstract
In this article, we study the representation and find all of the solutions of natural numbers and that can be represented in the form where and , where . We also show that satisfies , for all , and satisfies for all . Keywords : floor representation of the natural numbersReferences
Farhi, B. (2013) On the Representation of the Natural Numbers as the Sum of Three Terms of the Sequence
⌊ n^2/(a )⌋. Journal of Integer Sequences, 16, 13.6.3.
Farhi, B. (2014) An Elementary Proof that any Natural Number can be Written as the Sum of Three Terms of
the Sequence ⌊ n^2/(3 )⌋. Journal of Integer Sequences, 14,7.6.
Gilbert, W, J (1981) Radix Representation of Quadratic Fields. Journal of Mathematical Analysis and
Applications, 83(1), 264-274.
Matula, D, W. (1982) Basic Digit Sets for Radix Representation. Journal of ACM, 29(4), 1131-1143.
Reznick, B. (1989) Digital representations using the greatest integer functions. Transactions of the American
Mathematical Society, 312(1), 355-375.
Soufiane, M, Abdelmalek, A, and Ziane, M. (2014) On a conjecture of Farhi. Journal of Integer Sequences,
17, 14.1.8.
⌊ n^2/(a )⌋. Journal of Integer Sequences, 16, 13.6.3.
Farhi, B. (2014) An Elementary Proof that any Natural Number can be Written as the Sum of Three Terms of
the Sequence ⌊ n^2/(3 )⌋. Journal of Integer Sequences, 14,7.6.
Gilbert, W, J (1981) Radix Representation of Quadratic Fields. Journal of Mathematical Analysis and
Applications, 83(1), 264-274.
Matula, D, W. (1982) Basic Digit Sets for Radix Representation. Journal of ACM, 29(4), 1131-1143.
Reznick, B. (1989) Digital representations using the greatest integer functions. Transactions of the American
Mathematical Society, 312(1), 355-375.
Soufiane, M, Abdelmalek, A, and Ziane, M. (2014) On a conjecture of Farhi. Journal of Integer Sequences,
17, 14.1.8.
Downloads
Published
2019-09-30
Issue
Section
Research Article
