Antimagic labeling of forests with sets of consecutive integers

2022 ◽  
Vol 309 ◽  
pp. 75-84
Author(s):  
Eranda Dhananjaya ◽  
Wei-Tian Li
Keyword(s):  
Antimagic Labeling ◽  
Consecutive Integers

scholarly journals On the Ternary Exponential Diophantine Equation Equating a Perfect Power and Sum of Products of Consecutive Integers

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1813
Author(s):  
S. Subburam ◽  
Lewis Nkenyereye ◽  
N. Anbazhagan ◽  
S. Amutha ◽  
M. Kameswari ◽  
...  
Keyword(s):  
Positive Integer ◽  
Diophantine Equation ◽  
Upper Bound ◽  
Exponential Diophantine Equation ◽  
Research Article ◽  
All Solutions ◽  
Sum Of Products ◽  
Consecutive Integers ◽  
Sums Of Products ◽  
Positive Integers

Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In 2016, a research article, entitled – ’power values of sums of products of consecutive integers’, primarily proved the inequality n= 19,736 to obtain all solutions (x,y,n) of the equation for the fixed positive integers k≤10. In this paper, we improve the bound as n≤ 10,000 for the same case k≤10, and for any fixed general positive integer k, we give an upper bound depending only on k for n.

On triplets with descending largest prime factors

2001 ◽  
Vol 38 (1-4) ◽  
pp. 45-50 ◽  
Author(s):  
A. Balog
Keyword(s):  
Prime Factor ◽  
Prime Factors ◽  
Consecutive Integers

For an integer n≯1 letP(n) be the largest prime factor of n. We prove that there are infinitely many triplets of consecutive integers with descending largest prime factors, that is P(n - 1) ≯P(n)≯P(n+1) occurs for infinitely many integers n.

Note on Pairs of Consecutive Integers the Sum of whose Squares is an Integral Square

1902 ◽  
Vol 23 ◽  
pp. 264-267
Author(s):  
Thomas Muir
Keyword(s):  
Consecutive Integers

The solution of the problem of finding such pairs of integers is not a thing of yesterday, as may be seen by consulting Hutton's translation of Ozanam's Recreations, i. pp. 46–8 (1814).

scholarly journals Enumeration of the Edge Weights of Symmetrically Designed Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Muhammad Javaid ◽  
Hafiz Usman Afzal ◽  
Ebenezer Bonyah
Keyword(s):  
Disjoint Union ◽  
Antimagic Labeling ◽  
Pancyclic Graphs

The idea of super a , 0 -edge-antimagic labeling of graphs had been introduced by Enomoto et al. in the late nineties. This article addresses super a , 0 -edge-antimagic labeling of a biparametric family of pancyclic graphs. We also present the aforesaid labeling on the disjoint union of graphs comprising upon copies of C 4 and different trees. Several problems shall also be addressed in this article.

scholarly journals Almost perfect powers in consecutive integers

2001 ◽  
Vol 99 (1) ◽  
pp. 13-25 ◽  
Author(s):  
G. Hanrot ◽  
N. Saradha ◽  
T. N. Shorey
Keyword(s):  
Consecutive Integers

Super face d-antimagic labeling for disjoint union of toroidal fullerenes

2016 ◽  
Vol 55 (3) ◽  
pp. 849-863 ◽  
Author(s):  
Shahid Imran ◽  
Muhammad Hussain ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Numan
Keyword(s):  
Disjoint Union ◽  
Antimagic Labeling

Antimagic Labeling of Complete m-ary Trees

2002 ◽  
pp. 77-80
Author(s):  
P. D. Chawathe ◽  
Vijaya Krishna
Keyword(s):  
Antimagic Labeling
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