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A family of sequences. (English)
Aust. Sr. Math. J. 23, No. 1, 58-62 (2009).
Summary: Perhaps a business colleague threw out a challenge. The year: around 1200. The place: Pisa. The challenge: Calculate how many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on. The question and its solution found its way into the book "Liber abaci" by Leonardo of Pisa (known as Fibonacci), completed in 1202. It gives rise to the Fibonacci sequence. A colleague of the author issued the challenge: Prove that the sum of the squares of any two consecutive terms of the Fibonacci sequence is a term of the sequence. In this article, the author gives a more general context in which the sum of consecutive squares property is true, and a surprising connection with Pythagorean triples. (ERIC)
Classification: F65
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