Open AccessBook
Elementary Number Theory
Reads0
Chats0
TLDR
In this paper, the authors present a theory of divisibility theory in the Integers, which is based on the Fermat Conjecture of the Quadratic Reciprocity Law.Abstract:
1. Some Preliminary Considerations. 2. Divisibility Theory in the Integers. 3. Primes and Their Distribution. 4. The Theory of Congruences. 5. Fermat's Theorem. 6. Number-Theoretic Functions. 7. Euler's Generalization of Fermat's Theorem. 8. Primitive Roots and Indices. 9. The Quadratic Reciprocity Law. 10. Perfect Numbers. 11. The Fermat Conjecture. 12. Representation of Integers as Sums of Squares. 13. Fibonacci Numbers. 14. Continued Fractions. 15. Some Twentieth-Century Developments.read more
Citations
More filters
Journal ArticleDOI
Pseudo-random sequences and arrays
TL;DR: A simple description of pseudo-random sequences, or maximal-length shift-register sequences, and two-dimensional arrays of area n = 2lm- 1 with the same property.
Journal ArticleDOI
Distributed Consensus With Limited Communication Data Rate
TL;DR: It is proved that under the protocol designed, for a connected network, average consensus can be achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step.
Journal ArticleDOI
The behaviour of eigenstates of arithmetic hyperbolic manifolds
Zeév Rudnick,Peter Sarnak +1 more
TL;DR: In this paper, it was shown that the random wave model for eigenstates does not apply universally in 3 degrees of freedom for arithmetic hyperbolic manifolds, and that there is no strong localization (scarring) onto totally geodesic submanifolds.
Journal ArticleDOI
Entangled Networks, Synchronization, and Optimal Network Topology
TL;DR: A new family of graphs, entangled networks, with optimal properties in many respects, is introduced, such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc.
Book
Elementary Methods in Number Theory
TL;DR: Nathanson as mentioned in this paper gave a first course in number theory for students with no previous knowledge of the subject, which included divisibility, prime numbers, and congruences.
References
More filters
Journal ArticleDOI
Elementary number theory
TL;DR: The book as mentioned in this paper is designed for a first course in number theory with minimal prerequisites and is designed to stimulate curiosity about numbers and their properties, including almost a thousand imaginative exercises and problems.
Journal ArticleDOI
A History of Greek Mathematics
TL;DR: Heath as mentioned in this paper presents a history of Greek mathematics, from Thales to Euclid, from Aristarchus to Diophantus, with a focus on the historical aspect of science; it is for all lovers of Greek, for mathematics is a true legacy of Greece, and is interwoven through and through with Greek thought and philosophy.
Journal ArticleDOI
A Source Book in Mathematics
TL;DR: Smith as discussed by the authors presents the most significant passages from the works of the most important contributors to mathematics during the last three or four centuries, with the aim of presenting a very entertaining volume, a surprisingly successful attempt to do what nearly all good judges would have declared to be impossible.