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Mathematics Seminar Notes, 1978
Define the sequence \(\{R_n\}\) by integers \(R_0\), \(R_1\), and the recurrence relation \(R_n=2R_{n-1}+R_{n-2}\) \((n>1)\). If the equation \(x^2-2y^2=N\) has integer solutions, then all the solutions are given by finitely many sequences \(\{R_n\}\) and \((x;y)=\left(\pm (R_{2n}+R_{2n+1}); \pm R_{2n+1}\right)\).
Kiss, Péter, Várnai, Ferenc
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Define the sequence \(\{R_n\}\) by integers \(R_0\), \(R_1\), and the recurrence relation \(R_n=2R_{n-1}+R_{n-2}\) \((n>1)\). If the equation \(x^2-2y^2=N\) has integer solutions, then all the solutions are given by finitely many sequences \(\{R_n\}\) and \((x;y)=\left(\pm (R_{2n}+R_{2n+1}); \pm R_{2n+1}\right)\).
Kiss, Péter, Várnai, Ferenc
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The Fibonacci Quarterly, 1972
Pell numbers are generated by the sequence \(P_{n+2} = 2P_{n+1} + P_n\) \((P_0 = 0,\ P_1 = 1)\) and the solution in integers of the equation \(x^2 + y^2 = z^2\) is given by \(x = 2pq\), \(y = p^2 - q^2\). Let \(y - x = \pm c\). The author states that when \(c =1\) the values of \(p\) and \(q\) are Pell numbers and shows that when \(c \ne1\) then the ...
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Pell numbers are generated by the sequence \(P_{n+2} = 2P_{n+1} + P_n\) \((P_0 = 0,\ P_1 = 1)\) and the solution in integers of the equation \(x^2 + y^2 = z^2\) is given by \(x = 2pq\), \(y = p^2 - q^2\). Let \(y - x = \pm c\). The author states that when \(c =1\) the values of \(p\) and \(q\) are Pell numbers and shows that when \(c \ne1\) then the ...
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2014
Like Fibonacci and Lucas numbers, the Pell family is ubiquitous. Pell and Pell–Lucas numbers also provide boundless opportunities to experiment, explore, and conjecture; they are a lot of fun for inquisitive amateurs and professionals alike. In this chapter, we formally introduce the family, and cite their occurrences in earlier chapters, as well as ...
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Like Fibonacci and Lucas numbers, the Pell family is ubiquitous. Pell and Pell–Lucas numbers also provide boundless opportunities to experiment, explore, and conjecture; they are a lot of fun for inquisitive amateurs and professionals alike. In this chapter, we formally introduce the family, and cite their occurrences in earlier chapters, as well as ...
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Generalized Identities for third order Pell Number, Pell-Lucas Number and Modified Pell Number
2020วารสารวิทยาศาสตร์และเทคโนโลยี มทร.ธัญบุรี, 10, 1, 96 ...
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Common Factors of Pell and Pell-Lucas numbers
2021Progress in Applied Science and Technology, 11, 1, 7 ...
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On k-Pell hybrid numbers [PDF]
Journal of Discrete Mathematical Sciences and Cryptography, 2019 The aim of this work is to introduce a new sequence of numbers called k-Pell hybrid numbers and the presentation of some algebraic properties involving this sequence. In addition, we present the Binet formula, the generating functions and some identities
Paula Catarino
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On The Properties Of New Families Of Pell And Pell-Lucas Numbers.
Ars Comb., 2014In this paper, new families of Pell and Pell-Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for k = 2.
Gokkaya, Havva, Uslu, Kemal
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A Problem of Diophantus and Pell Numbers
1998Several Diophantine quadruples in terms of Pell numbers are constructed using general construction of Diophantine quadruples with property D(l^2).
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Integral representations of the Pell and Pell-Lucas numbers
Journal of Science and Science Education, 7, 2, 272 ...openaire +1 more source