Abstract
The axiom of mathematical induction is used extensively as a method of proof in mathematics. This chapter presents inductive proofs of results that may not be known to the reader. We begin with a short review of mathematical induction (Sect. 6.1). Section 6.2 proves results about the familiar Fibonacci numbers while Sect. 6.3 proves results about Fermat numbers. Section 6.4 presents the 91-function discovered by John McCarthy; the proof is by induction on an unusual sequence: integers in an inverse ordering. The proof of the formula for the Josephus problem (Sect. 6.5) is also unusual because of the double induction on two different parts of an expression.
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Ben-Ari, M. (2022). Induction. In: Mathematical Surprises. Springer, Cham. https://doi.org/10.1007/978-3-031-13566-8_6
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DOI: https://doi.org/10.1007/978-3-031-13566-8_6
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Publisher Name: Springer, Cham
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