On the problem of the F.Smarandache factor
Liu Bao-li
Abstract
Liu Bao-li
Abstract
For any positive integer n1,if n=d1d1…dk,where di(i=1,2,…,k) is the divisor of n,then d1d2…dk are a F.Smarandache factor partitions of n.Using the elementary and combinational methods,the computational problem of F(1#n) for some special positive integers is studied,and an exact computational formula is given.Finally,two conjectures proposed by Amarnath Murthy and Charles Ashbacher in reference are solved.
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For any positive integer n1,if n=d1d1…dk,where di(i=1,2,…,k) is the divisor of n,then d1d2…dk are a F.Smarandache factor partitions of n.Using the elementary and combinational methods,the computational problem of F(1#n) for some special positive integers is studied,and an exact computational formula is given.Finally,two conjectures proposed by Amarnath Murthy and Charles Ashbacher in reference are solved.
Key concepts: Mathematics, Integer (computer science), Divisor (algebraic geometry), Greatest common divisor, Combinatorics, Factor (programming language), Multiple, Discrete mathematics