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Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/22959
Title: On Moessner's Theorem
Authors: Kozen, Dexter
Silva, Alexandra
Keywords: Moessner's theorem
Issue Date: 12-Jun-2011
Abstract: Moessner's theorem describes a procedure for generating a sequence of n integer sequences that lead unexpectedly to the sequence of nth powers 1^n, 2^n, 3^n, ... Paasche's theorem is a generalization of Moessner's; by varying the parameters of the procedure, one can obtain the sequence of factorials 1!, 2!, 3!, ... or the sequence of superfactorials 1!!, 2!!, 3!!, ... Long's theorem generalizes Moessner's in another direction, providing a procedure to generate the sequence a, (a+d)2^{n-1}, (a+2d)3^{n-1}, ... Proofs of these results in the literature are typically based on combinatorics of binomial coefficients or calculational scans. In this note we give a short and revealing algebraic proof of a general theorem that contains Moessner's, Paasche's, and Long's as special cases. We also prove a generalization that gives new Moessner-type theorems.
URI: http://hdl.handle.net/1813/22959
Appears in Collections:Computing and Information Science Technical Reports

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