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Number Theory Jeremy Avigad, Kevin Donnelly, David Gray, Adam Kramer,
 

Summary: Number Theory
Jeremy Avigad, Kevin Donnelly, David Gray, Adam Kramer,
Lawrence C. Paulson, Paul Raff, Thomas M. Rasmussen, Christophe Tabaczync
September 10, 2004
Contents
1 Permutations 6
1.1 Some examples of rule induction on permutations . . . . . . . 6
1.2 Ways of making new permutations . . . . . . . . . . . . . . . 7
1.3 Further results . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Removing elements . . . . . . . . . . . . . . . . . . . . . . . . 8
2 The Greatest Common Divisor and Euclid's algorithm 10
3 The Fibonacci function 14
4 Fundamental Theorem of Arithmetic (unique factorization
into primes) 17
4.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3 Prime list and product . . . . . . . . . . . . . . . . . . . . . . 18
4.4 Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.5 Permutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.6 Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

  

Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University

 

Collections: Multidisciplinary Databases and Resources; Mathematics