Pell numbers whose Euler function is a Pell number
نویسندگان
چکیده
منابع مشابه
Pell Numbers Whose Euler Function Is a Pell Number
We show that the only Pell numbers whose Euler function is also a Pell number are 1 and 2.
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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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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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The Greek mathematician Diophantus of Alexandria noted that the set { 1 16 , 33 16 , 17 4 , 105 16 } has the following property: the product of its any two distinct elements increased by 1 is a square of a rational number (see [3]). Fermat first found a set of four positive integers with the above property, and it was {1, 3, 8, 120}. In 1969, Davenport and Baker [2] showed that if positive inte...
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In this paper we present some identities involving terms of k-Pell, k-Pell-Lucas and Modified k-Pell sequences. We also give some results on the column and row norms of Hankel matrices which entries are numbers of these sequences. Mathematics Subject Classification: 11B37, 11B83, 15A60
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2017
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1715231f