SOFA 2014: Soft Computing Applications pp 403-411 | Cite as

Fermat Number Applications and Fermat Neuron

Conference paper
First Online:
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 356)

Abstract

This chapter presents Fermat numbers, and their applications to filtering, autocorrelation, and related areas with advantages over the conventional computing. This paper discusses the basic concepts of prime numbers like Mersenne primes and Fermat primes and their comparison for computing with advantage, modulo arithmetic, Galois field, and Chinese remainder theorem. It describes and applies transforms using these concepts and their advantages like fast computation with no round off or truncation errors. It also introduces a new paradigm in neural networks (NN), about the concept of Fermat neurons. This concept needs to be developed further, as it is promising for real-life applications.

Keywords

Fermat number Modulo arithmetic Mersenne number Chinese remainder theorem Galois field Fermat neuron XOR gate FPGA 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Kalasalingam UniversityKrishnankoilIndia
  2. 2.Aurel Vlaicu University of AradAradRomania

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