Corpus ID: 18388343

ON A DIGRAPH DEFINED BY SQUARING MODULO n

@inproceedings{Blanton2010ONAD,
  title={ON A DIGRAPH DEFINED BY SQUARING MODULO n},
  author={E. Blanton},
  year={2010}
}
Let us begin by defining the digraph Gn. We identify the vertices of Gn with the set {0, 1, 2, . .., n 1}. The ordered pair (a, b) is an edge of Gn if and only if a = b modulo n . Our general aim is to show how the numbertheoretic properties of n and n 1 are closely associated with certain "geometric" properties of the digraph Gn. The most fundamental results for prime moduli are established in Section 2. In Section 3 we are able to extend these results and at the same time to give a framework… Expand

Figures and Tables from this paper

A Classification of Cyclic Nodes and Enumeration of Components of a Class of Discrete Graphs
Let Zn be the ring of residue classes modulo n. Define f : Zn 㜡 Zn by f(x) = x 4 . Action of this map is studied by means of digraphs which produce an edge from the residue classes a to b if f(a) �Expand
Importance of Power Digraph in Computer Science
TLDR
In this note, some fields of interest are highlighted where power digraphs can be utilized in a more friendly way to entertain a layman without knowing much about its mathematics. Expand
Symmetry of iteration graphs
We examine iteration graphs of the squaring function on the rings ℤ/nℤ when n = 2kp, for p a Fermat prime. We describe several invariants associated to these graphs and use them to prove that theExpand
Error detection in number-theoretic and algebraic algorithms
CPU's are unreliable: at any point in a computation, a bit may be altered with some (small) probability. This probability may seem negligible, but for large calculations (i.e., months of CPU time),Expand

References

SHOWING 1-10 OF 22 REFERENCES
The problem of Sierpiński concerning ⋅2ⁿ+1
Let k0 be the least odd value of k such that k ■ 2" + 1 is composite for all n > 1. In this note, we present the results of some extensive computations which restrict the value of k0 to one of 119Expand
On the smallest such that all ⋅2ⁿ+1 are composite
In this note we present some computational results which restrict the least odd value of k such that k ■ 2" + 1 is composite for all n > 1 to one of 91 numbers between 3061 and 78557, inclusive.Expand
Monte Carlo Methods for Index Computation (mod p)
We describe some novel methods to compute the index of any integer relative to a given primitive root of a prime p. Our first method avoids the use of stored tables and apparently requires 0(p )Expand
An introduction to the theory of numbers
Divisibility congruence quadratic reciprocity and quadratic forms some functions of number theory some diophantine equations Farey fractions and irrational numbers simple continued fractions primesExpand
Elementary Number Theory
Designed for a first course in number theory with minimal prerequisites, the book is designed to stimulates curiosity about numbers and their properties. Includes almost a thousand imaginativeExpand
Solved and Unsolved Problems in Number Theory
When writing can change your life, when writing can enrich you by offering much money, why don't you try it? Are you still very confused of where getting the ideas? Do you still have no idea withExpand
History of the Theory of Numbers, Volume I: Divisibility and Primality
Known Primes with 1000 or More Digits
  • Known Primes with 1000 or More Digits
  • 1990
UBASIC: A Public Domain BASIC for Mathematics
  • Notices of the A.M.S
  • 1989
UBASIC: A Public Domain BASIC for Mathematics." Notices of the A.M.S
  • 1989
...
1
2
3
...