Photo from wikipedia
Let F n be the nth Fibonacci number. Order of appearance z ( n ) of a natural number n is defined as smallest natural number k, such that n… Click to show full abstract
Let F n be the nth Fibonacci number. Order of appearance z ( n ) of a natural number n is defined as smallest natural number k, such that n divides F k . In 1930, Lehmer proved that all solutions of equation z ( n ) = n ± 1 are prime numbers. In this paper, we solve equation z ( n ) = n + ℓ for | ℓ | ∈ { 1 , … , 9 } . Our method is based on the p-adic valuation of Fibonacci numbers.
Keywords:
fibonacci;
order;
equations related;
order appearance;
diophantine equations
Journal Title: Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!