Products of consecutive integers and the Markoff equation

1994 ◽  
Vol 48 (1) ◽  
pp. 120-120
Author(s):  
Arthur Baragar
Keyword(s):  
Markoff Equation ◽  
Consecutive Integers

Products of consecutive integers and the Markoff equation

1996 ◽  
Vol 51 (1-2) ◽  
pp. 129-136 ◽  
Author(s):  
Arthur Baragar
Keyword(s):  
Markoff Equation ◽  
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 Some Computations Between Sums of Powers of Consecutive Integers and Alternating Sums of Powers of Consecutive Integers

2019 ◽  
Vol 2 (2) ◽  
pp. 137-143
Author(s):  
Uğur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Sums Of Powers ◽  
Alternating Sums ◽  
Consecutive Integers

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

scholarly journals The Markoff equation X2 + Y2 + Z2 = aXYZ over quadratic imaginary fields

1990 ◽  
Vol 35 (1) ◽  
pp. 72-104 ◽  
Author(s):  
Joseph H. Silverman
Keyword(s):  
Quadratic Imaginary Fields ◽  
Markoff Equation

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
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