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pro vyhledávání: '"polygonal numbers"'
In this paper, we consider sums of three generalized $m$-gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions on $m$ modulo $30$, we show that a density one set of integers is repre
Externí odkaz:
http://arxiv.org/abs/2409.07895
Publikováno v:
Integers 23 (2023), A40
Recently, Jha (arXiv:2007.04243, arXiv:2011.11038) has found identities that connect certain sums over the divisors of $n$ to the number of representations of $n$ as a sum of squares and triangular numbers. In this note, we state a generalized result
Externí odkaz:
http://arxiv.org/abs/2409.02023
Autor:
Bhattacharya, Soumya, Rahaman, Habibur
For all integers $r,s>2$, there are infinitely many primes which can be written as the sum of an $r$-gonal number and an $s$-gonal number. In general, any linear combination of an $r$-gonal number and an $s$-gonal number with coprime positive integer
Externí odkaz:
http://arxiv.org/abs/2408.13650
Autor:
Li, Jialin, Wang, Haowu
In this paper we give unified formulas for the numbers of representations of positive integers as sums of four generalized $m$-gonal numbers, and as restricted sums of four squares under a linear condition, respectively. These formulas are given as $
Externí odkaz:
http://arxiv.org/abs/2405.14710
Akademický článek
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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:
Caglayan, Günhan1 (AUTHOR) gcaglayan@njcu.edu
Publikováno v:
Mathematical Intelligencer. Mar2023, Vol. 45 Issue 1, p38-41. 4p.
Autor:
Kane, Ben, Yang, Zichen
In this paper, we consider mixed sums of generalized polygonal numbers. Specifically, we obtain a finiteness condition for universality of such sums; this means that it suffices to check representability of a finite subset of the positive integers in
Externí odkaz:
http://arxiv.org/abs/2305.14670
Autor:
Kim, Byungchan1 (AUTHOR), Kim, Ji Young2 (AUTHOR), Lee, Chong Gyu3 (AUTHOR) cglee@ssu.ac.kr, Park, Poo-Sung4 (AUTHOR)
Publikováno v:
Aequationes Mathematicae. Aug2021, Vol. 95 Issue 4, p601-621. 21p.