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# Euler_Phi and Its Applications

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Euler_Phi.zip is a suite of the foll Programmes :

1) Euler_Phi (n) returns the no of positive integers less than n which are prime to n.

2) a_k_mod_m_LCM_Method (a, m, k) : Imagine computing mod(14^26, 45) or mod(56^3005, 1125).
This programme computes a_k_mod_m = mod (a^k, m) when a and m are coprime, using certain rules for the reduction of computations based on Euler_Phi.

3) b_n_mod_m_Rpt_Sq_Method (b, n, m) : Imagine computing mod(38^75, 103) or mod(38^75, 103). This programme computes b_n_mod_m = mod (b^n, m).
The diff between this pgm and a_k_mod_m_LCM_Method.m is that in a_k_mod_m_LCM_Method,
the inputs a and m are coprime ; here, in b_n_mod_m_Rpt_Sq_Method.m, it is not necessary that b and m need be coprime.

4) Verify_Euler_Phi(n) : This is a small programme to prove that n = sum of Euler_Phi taken over all divisors d of n.

Refer to Euler_Phi function in P15, P22, P23, Prob 21 & Prob 23 / (P26 + P205) in the book : A course in Number Theory and Cryptography by Neal Koblitz.

Free download from Shareware Connection - Euler_Phi (n) returns the no of positive integers less than n which are prime to n.

Publisher: Sundar Krishnan | License: Shareware
Version: 1.0 | Size: 10 KB | Platform: Matlab, Scripts
Released Date: 26-06-2013 | Rating: 0 | Title: Euler_Phi and Its Applications

Author Url: http://www.mathworks.com
Program Info Url: http://www.mathworks.com

Properties of Hermitian, Unitary, Positive Definite and Sparse Matrices - This file : eig_svd_herm_unit_pos_def_2.m is a modified (improved) version of my previous file

Generate many examples of Ramanujam's Diophantine Equation - This programme is about finding many examples of Ramanujam's Diophantine Equation

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Chinese Remainder Theorem for Polynomials - 15th July, 2005 : Poly_POWER.m is now corrected !

Euler_Phi and Its Applications keywords:

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Euler Circuits and Paths - Euler Circuits and Paths was created as a simple and user-friendly application that lets you examine Euler circuits and paths in arbitrary graphs.

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Ask Expert Script - The Ask an Expert script is yet another powerful application that facilitates questionnaire session between the visitors and the experts. The rating system allows users to rate questions and its corresponding answers based on user responses.

Shareware Connection periodically updates pricing and software information of 'Euler_Phi and Its Applications' from company source 'Sundar Krishnan' , so some information may be slightly out-of-date. You should confirm all information before relying on it. Software piracy is theft,  Using 'Euler_Phi and Its Applications' crack, password, serial numbers, registration codes, key generators is illegal and prevent future development of Euler_Phi and Its Applications.

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