99.27 A relationship between Pell numbers and triangular square numbers
نویسندگان
چکیده
منابع مشابه
Some New Properties of Balancing Numbers and Square Triangular Numbers
A number N is a square if it can be written as N = n2 for some natural number n; it is a triangular number if it can be written as N = n(n + 1)/2 for some natural number n; and it is a balancing number if 8N2 +1 is a square. In this paper, we study some properties of balancing numbers and square triangular numbers.
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1. BALANCING NUMBERS We call an Integer n e Z a balancing number if 1+ 2+ --+ (»l ) = (w + l) + (w + 2) +••• + (» + >•) (1) for some r e Z. Here r is called the balancer corresponding to the balancing number n. For example, 6, 35, and 204 are balancing numbers with balancers 2, 14, and 84, respectively. It follows from (1) that, if n is a balancing number with balancer r, then n2^(n + r)(n + r ...
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In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text.
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We study a relation between factorials and their additive analog, the triangular numbers. We show that there is a positive integer k such that n! = 2kT where T is a product of triangular numbers. We discuss the primality of T±1 and the primality of |T − p| where p is either the smallest prime greater than T or the greatest prime less than T .
متن کاملThe sum and product of Fibonacci numbers and Lucas numbers, Pell numbers and Pell-Lucas numbers representation by matrix method
Denote by {Fn} and {Ln} the Fibonacci numbers and Lucas numbers, respectively. Let Fn = Fn × Ln and Ln = Fn + Ln. Denote by {Pn} and {Qn} the Pell numbers and Pell-Lucas numbers, respectively. Let Pn = Pn × Qn and Qn = Pn + Qn. In this paper, we give some determinants and permanent representations of Pn, Qn, Fn and Ln. Also, complex factorization formulas for those numbers are presented. Key–Wo...
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ژورنال
عنوان ژورنال: The Mathematical Gazette
سال: 2015
ISSN: 0025-5572,2056-6328
DOI: 10.1017/mag.2015.89