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Article: Smarandache "Chopped" [N.sup.N] and N + [1.sup.N-1].
- Article from:
- Scientia Magna
- Article date:
- January 1, 2005
- Author:
CopyrightCOPYRIGHT 2005 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Florentin Smarandache has posed many problems that deal with perfect powers. See [1] for example. Perfect powers of the form [N.sup.N] are aesthetically pleasing because of their symmetry. But in my opinion they would be more agreeable if their number of decimal digits (their "length" in base-10 representation) were equal to N. In this note we will considere numbers of the form [N.sup.N] and N - [1.sup.N+1] that have been "chopped off" to have N decimal digits. We will refer to these numbers as Smarandache Chopped [N.sup.N] numbers, and Smarandache Chopped N - [1.sup.N+1] numbers; and we will investigate them to see if 1) they are prime, 2) they are automorphic.
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