scholarly journals An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers

2011 ◽  
Vol 87 (4) ◽  
pp. 45-50 ◽  
Author(s):  
Florian Luca ◽  
Roger Oyono
Keyword(s):  
Diophantine Equation ◽  
Fibonacci Numbers ◽  
Exponential Diophantine Equation

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.

scholarly journals Solving an exponential Diophantine equation

2010 ◽  
Vol 144 (4) ◽  
pp. 315-322
Author(s):  
Mario Huicochea
Keyword(s):  
Diophantine Equation ◽  
Exponential Diophantine Equation
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