Displaying 161 – 180 of 239

Showing per page

On the intersection of two distinct k -generalized Fibonacci sequences

Diego Marques (2012)

Mathematica Bohemica

Let k 2 and define F ( k ) : = ( F n ( k ) ) n 0 , the k -generalized Fibonacci sequence whose terms satisfy the recurrence relation F n ( k ) = F n - 1 ( k ) + F n - 2 ( k ) + + F n - k ( k ) , with initial conditions 0 , 0 , , 0 , 1 ( k terms) and such that the first nonzero term is F 1 ( k ) = 1 . The sequences F : = F ( 2 ) and T : = F ( 3 ) are the known Fibonacci and Tribonacci sequences, respectively. In 2005, Noe and Post made a conjecture related to the possible solutions of the Diophantine equation F n ( k ) = F m ( ) . In this note, we use transcendental tools to provide a general method for finding the intersections F ( k ) F ( m ) which gives evidence supporting...

On the Lebesgue-Nagell equation

Andrzej Dąbrowski (2011)

Colloquium Mathematicae

We completely solve the Diophantine equations x ² + 2 a q b = y (for q = 17, 29, 41). We also determine all C = p a p k a k and C = 2 a p a p k a k , where p , . . . , p k are fixed primes satisfying certain conditions. The corresponding Diophantine equations x² + C = yⁿ may be studied by the method used by Abu Muriefah et al. (2008) and Luca and Togbé (2009).

Currently displaying 161 – 180 of 239