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Simplified method of finding the remainder and its usability in certain types of problems

Published on May 2012 by Anshul Vikram Pandey
National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
Foundation of Computer Science USA
RTMC - Number 12
May 2012
Authors: Anshul Vikram Pandey
b9326f8c-53ca-456e-bc26-5da81252bd7c

Anshul Vikram Pandey . Simplified method of finding the remainder and its usability in certain types of problems. National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011. RTMC, 12 (May 2012), 16-20.

@article{
author = { Anshul Vikram Pandey },
title = { Simplified method of finding the remainder and its usability in certain types of problems },
journal = { National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011 },
issue_date = { May 2012 },
volume = { RTMC },
number = { 12 },
month = { May },
year = { 2012 },
issn = 0975-8887,
pages = { 16-20 },
numpages = 5,
url = { /proceedings/rtmc/number12/6709-1107/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
%A Anshul Vikram Pandey
%T Simplified method of finding the remainder and its usability in certain types of problems
%J National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
%@ 0975-8887
%V RTMC
%N 12
%P 16-20
%D 2012
%I International Journal of Computer Applications
Abstract

Remainder theorems are very popular for finding the remainder in various types of problems. In this paper, we have proposed a simplified approach of finding the remainder using basic mathematics. This method is very effective in solving certain types of problems which involve exponentiation of dividend by some positive integer and those which have common factors in their dividend and divisor. Here, we have discussed how the individual factors of the dividend can be used to find the remainder. This method is easy to understand and leads to faster remainder computation, using simple calculations and works very effectively for big dividends as well. The proof of this method is given along with an example to explain its working for both types of problems. The concept of negative remainder and repetitive application of the simplified method are also discussed.

References
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  2. M. Mignotte. How to Share a Secret. : Lecture Notes in Computer Science, Volume 149/1983, 371-375, (1983)
  3. J. Mitchell. Cryptography, briey. : 802. 11b slides from Dan Boneh, Stanford University, USA Spring (2002)
  4. P. Rudnicki . Little B_ezout Theorem (Factor Theorem). Formalized Mathematics 12 (1): 49} U58, (2004)
  5. Y. Sung-Ming, K. Seungjoo, L. Seongan, M. Sang-Jae. : RSA speedup with Chinese remainder theorem immune against hardware fault cryptanalysis. Computers, IEEE Trans. , Volume: 52 Issue:4, 461 - 472, April (2003).
  6. T. Van Vu. : E_cient Implementations of the Chinese Remainder Theorem for Sign Detection and Residue Decoding. Computers, IEEE Trans. , Volume: C-34 Issue: 7, 646 - 651, August (2006)
  7. Chinese remainder theorem: http://en:wikipedia:org/wiki/Chineseremaindertheorem
  8. Factor Theorem, http://en. wikipedia. org/wiki/Factor_theorem
  9. Little Bezout Theorem or Polynomial Remainder Theorem, http://en. wikipedia. org/wiki/Polynomial_remainder_theorem
Index Terms

Computer Science
Information Sciences

Keywords

Simplified Remainder Computation Exponential Dividend Negative Remainder Remainder Algorithm Speed Calculation