Amin Witno

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 19, 2013, Number 3, Pages 66—69

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## Details

### Authors and affiliations

Amin Witno

*Department of Basic Sciences
Philadelphia University, 19392 Jordan
*

### Abstract

We show that the sequence *w ^{k}* mod

*n*, given that gcd(

*w*,

*n*) > 1, can reach a maximal cycle length of

*ϕ*(

*n*) if and only if

*n*is twice an odd prime power,

*w*is even, and

*w*is a primitive root modulo

*n*=2.

### Keywords

- Modular exponentiation
- Primitive roots

### AMS Classification

- 11A05
- 11A07

### References

- Dummit, D. S., R. M. Foote, Abstract Algebra, 3rd ed., Wiley, 2003.
- Witno, A. Theory of Numbers, BookSurge Publishing, 2008.

## Related papers

## Cite this paper

APAWitno, A. (2013). Modular zero divisors of longest exponentiation cycle. Notes on Number Theory and Discrete Mathematics, 19(3), 66-69.

ChicagoWitno, Amin. “Modular Zero Divisors of Longest Exponentiation Cycle.” Notes on Number Theory and Discrete Mathematics 19, no. 3 (2013): 66-69.

MLAWitno, Amin. “Modular Zero Divisors of Longest Exponentiation Cycle.” Notes on Number Theory and Discrete Mathematics 19.3 (2013): 66-69. Print.