Zobrazeno 1 - 10
of 293
pro vyhledávání: '"11A99"'
Autor:
Kay, Anthony, Downes-Ward, Katrina
We develop a classification of the fixed points and cycles of the Kaprekar transformation in even bases. The most numerous fixed points and cycles are those we denote symmetric and almost-symmetric; the structure of the cycles of these classes in bas
Externí odkaz:
http://arxiv.org/abs/2408.12257
Autor:
Goodman-Strauss, Chaim
Through a series of elementary exercises, we explain the fractal structure of Pascal's triangle when written modulo $p$ using an 1852 theorem due to Kummer: A prime $p$ divides $\dfrac {n!}{i!j!} $ if and only if there is a carry in the addition $i+j
Externí odkaz:
http://arxiv.org/abs/2405.13060
Autor:
Schäfer, Leo, Vigolo, Federico
We introduce a coarse algebraic invariant for coarse groups and use it to differentiate various coarsifications of the group of integers. This lets us answer two questions posed by Leitner and the second author. The invariant is obtained by consideri
Externí odkaz:
http://arxiv.org/abs/2404.08536
Autor:
Bradford, Kyle
This paper makes the following conjecture: For every prime $p$ there exists a positive integer $x$ with $\left\lceil \frac{p}{4} \right\rceil \leq x \leq \left\lceil \frac{p}{2} \right\rceil$ and a positive divisor $d|x^2$ so that either: (1) $ d \bm
Externí odkaz:
http://arxiv.org/abs/2403.16047
Autor:
Somu, Sai Teja, Tran, Duc Van Khanh
Publikováno v:
Journal of Integer Sequences, 27(5), Article 24.5.1, 2024
Practical numbers are positive integers $n$ such that every positive integer less than or equal to $n$ can be written as a sum of distinct positive divisors of $n$. In this paper, we show that all positive integers can be written as a sum of a practi
Externí odkaz:
http://arxiv.org/abs/2403.13533
Autor:
Weisenberg, Desmond
An additive-multiplicative magic square is a square grid of numbers whose rows, columns, and long diagonals all have the same sum (called the magic sum) and the same product (called the magic product). There are numerous open problems about magic squ
Externí odkaz:
http://arxiv.org/abs/2311.06326
Autor:
Guo, Yanqiu, Ilyin, Michael
This paper is inspired by Richards' work on large gaps between sums of two squares [10]. It is shown in [10] that there exist arbitrarily large values of $\lambda$ and $\mu$, where $\mu \geq C \log \lambda$, such that intervals $[\lambda, \,\lambda +
Externí odkaz:
http://arxiv.org/abs/2309.10971
Autor:
Sanna, Carlo
Let $(F_n)_{n \geq 1}$ be the sequence of Fibonacci numbers. For all integers $a$ and $b \geq 1$ with $\gcd(a, b) = 1$, let $[a^{-1} \!\bmod b]$ be the multiplicative inverse of $a$ modulo $b$, which we pick in the usual set of representatives $\{0,
Externí odkaz:
http://arxiv.org/abs/2306.08382
Autor:
Jakimczuk Rafael
Publikováno v:
Annales Mathematicae Silesianae, Vol 38, Iss 2, Pp 314-335 (2024)
We prove a theorem which unifies some formulas, for example the counting function, of some sets of numbers including all positive integers, h-free numbers, h-full numbers, etc. We also establish a conjecture and give some examples where the conjectur
Externí odkaz:
https://doaj.org/article/81d89c1aa96d457b8939219c015039a7
Autor:
Zhu, Yongwen
For two integers $a$ and $b$, the plum-blossom product of $a$ and $b$ is defined as the ones of the usual product of $a$ and $b$ if the ones is less than or equal to $3$, or otherwise as the ones minus $10$. Under this operation, all integers is a co
Externí odkaz:
http://arxiv.org/abs/2301.05822