MODULAR TRIBONACCI NUMBERS BY MATRIX METHOD
نویسندگان
چکیده
منابع مشابه
On the sum of reciprocal Tribonacci numbers
In this paper we consider infinite sums derived from the reciprocals of the Fibonacci numbers, and infinite sums derived from the reciprocals of the square of the Fibonacci numbers. Applying the floor function to the reciprocals of these sums, we obtain equalities that involve the Fibonacci numbers.
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In this paper, we use a simple method to derive di¤erent recurrence relations on the Tribonacci numbers and their sums. By using the companion matrices and generating matrices, we get more identities on the Tribonacci numbers and their sums, which are more general than that given in literature [E. Kilic, Tribonacci Sequences with Certain Indices and Their Sum, Ars Combinatoria 86 (2008), 13-22....
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We find a new Tribonacci-like sequence of positive integers 〈x0, x1, x2, . . .〉 given by xn = xn−1 + xn−2 + xn−3 , n ≥ 3, and gcd(x0, x1, x2) = 1 that contains no prime numbers. We show that the sequence with initial values x0 = 151646890045, x1 = 836564809606, x2 = 942785024683 is the current record in terms of the number of digits.
متن کاملIncomplete generalized Tribonacci polynomials and numbers
The main object of this paper is to present a systematic investigation of a new class of polynomials – incomplete generalized Tribonacci polynomials and a class of numbers associated with the familiar Tribonacci polynomials. The various results obtained here for these classes of polynomials and numbers include explicit representations, generating functions, recurrence relations and summation fo...
متن کاملTribonacci Numbers and the Brocard - Ramanujan Equation
Let (Tn)n≥0 be the Tribonacci sequence defined by the recurrence Tn+2 = Tn+1 + Tn + Tn−1, with T0 = 0 and T1 = T2 = 1. In this short note, we prove that there are no integer solutions (u,m) to the Brocard-Ramanujan equation m! + 1 = u2 where u is a Tribonacci number.
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ژورنال
عنوان ژورنال: The Pure and Applied Mathematics
سال: 2013
ISSN: 1226-0657
DOI: 10.7468/jksmeb.2013.20.3.207