We give the answer to the question in the title by proving that is the largest Lucas number expressible as a sum of exactly three repdigits. Therefore, there are many Lucas numbers which are sums of three repdigits.
In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
The purpose of this paper is to prove that the common terms of linear recurrences and have at most common terms if , and have at most three common terms if where and are fixed positive integers and is a prime, such that neither nor is perfect square, further are nonzero integers satisfying the equations and .