Abstract
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 some of their fundamental properties. In Chapter 12, we will find geometric interpretations of both Pell and Pell–Lucas numbers, and in Chapter 16 some combinatorial interpretations.
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Notes
- 1.
Based on the 1994 William L. Putnam Mathematical Competition, Mathematical Association of America [4] .
- 2.
† | M| denotes the determinant of the square matrix M.
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Koshy, T. (2014). Pell and Pell–Lucas Numbers. In: Pell and Pell–Lucas Numbers with Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8489-9_7
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DOI: https://doi.org/10.1007/978-1-4614-8489-9_7
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