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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Burton DM (1991) Elementary number theory, Universal Book Stall, New Delhi
Arya SP (1989) Fermat numbers. Math Educ 6(1):5–6
Arya SP (1990) More about Fermat numbers. Math Educ 7(2):139–141
Manakov A (2010) Development of FPGA-based digital correlator using Fermat number transform, master Thesis, (supervisor: Dr. Tomsk State University, Oleg Pono-ma-rev)
Agarwal RC, Burrus CS (1975) Number theoretic transforms to implement fast digital convolutions. Proc IEEE 63(4):550–560
Kekre HB, Madan VK (1988) Application of rader transform to the analysis of nuclear spectral data. Nucl Instrum Methods A269:279–281
Bose BK (2007) Neural network applications in power electronics and motor drives—an introduction and perspective. IEEE Trans Industrial Electron 54(1), 2007
Minsky M, Papert S (1968) Perceptron, MIT Press. Mass, Cambridge
Graupe D (2013) Principles of artificial neural networks, 3rd edn. World Scientific Publishing Company, Singapore, 19 Nov 2013
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Madan, V.K., Balas, M.M., Radhakrishnan, S. (2016). Fermat Number Applications and Fermat Neuron. In: Balas, V., C. Jain, L., Kovačević, B. (eds) Soft Computing Applications. SOFA 2014. Advances in Intelligent Systems and Computing, vol 356. Springer, Cham. https://doi.org/10.1007/978-3-319-18296-4_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-18296-4_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18295-7
Online ISBN: 978-3-319-18296-4
eBook Packages: EngineeringEngineering (R0)