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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
Download Url: http://www.mathworks.com/matlabcentral/fx_files/5887/1/Euler_Phi_1.zip

More downloads from Euler_Phi and Its Applications publisher Sundar Krishnan:

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

Factoring Techniques, MPN and FPN - MPN_FPN.m : This programme creates Mersenne Prime Numbers and Fermat Prime Numbers.

GCD of Polynomials and Polynomials raised to some Power including Fractional Power - If we need to verify the fact that a Polynomial has multiple roots iff (if and only if) it has a common factor with it's derivative, we need two things

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

Euler_Phi and Its Applications keywords:
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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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