On repdigits as product of consecutive Fibonacci
... where F0 = 0 and F1 = 1. These numbers are well-known for possessing amazing properties. In 1963, the Fibonacci Association was created to provide an opportunity to share ideas about these intriguing numbers and their applications. We remark that, in 2003, Bugeaud et al. [2] proved that the only per ...
... where F0 = 0 and F1 = 1. These numbers are well-known for possessing amazing properties. In 1963, the Fibonacci Association was created to provide an opportunity to share ideas about these intriguing numbers and their applications. We remark that, in 2003, Bugeaud et al. [2] proved that the only per ...
Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae 31
... 17 once |x| ≥ 240. The method presented in [8] is elementary, and the computations were done using congruences with respect to small moduli. The purpose of this note is two fold. First of all, we improve the lower bound from [8] by showing that P (x2 + 1) ≥ 101 once |x| ≥ 24208145. Secondly, our met ...
... 17 once |x| ≥ 240. The method presented in [8] is elementary, and the computations were done using congruences with respect to small moduli. The purpose of this note is two fold. First of all, we improve the lower bound from [8] by showing that P (x2 + 1) ≥ 101 once |x| ≥ 24208145. Secondly, our met ...
Modular forms and Diophantine questions
... assertion that is true experimentally may have one or more counterexamples that happen to be very large. In fact, assertions that realize this possibility are not hard to find in number theory. As Fermat himself knew, the first solution to x2 −109y 2 = 1 in positive integers x and y is given by x = ...
... assertion that is true experimentally may have one or more counterexamples that happen to be very large. In fact, assertions that realize this possibility are not hard to find in number theory. As Fermat himself knew, the first solution to x2 −109y 2 = 1 in positive integers x and y is given by x = ...
