Homework No.3

[Advanced Control Flow]

Find the number of your Homework No.3 calculating the expression: (Faculty_Number % 21). Your task is to implement in C++ the algorithm described in your number.

Number Theory

(0) Prime Factorization Algorithm
http://en.wikipedia.org/wiki/Prime_factorization_algorithm

(1) Sieve of Eratosthenes [P7.8]
http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

(2) Integer factorization [P7.7]
http://en.wikipedia.org/wiki/Integer_factorization

(3) Fermat primality test
http://en.wikipedia.org/wiki/Fermat_primality_test

(4) Miller-Rabin primality test
http://en.wikipedia.org/wiki/Miller-Rabin_primality_test

(5) Solovay-Strassen primality test
http://en.wikipedia.org/wiki/Solovay-Strassen_primality_test

(6) Euclidean algorithm
http://en.wikipedia.org/wiki/Euclidean_algorithm

(7) Least common multiple
http://en.wikipedia.org/wiki/Least_common_multiple

(8) Coprime
http://en.wikipedia.org/wiki/Coprime

Numerical Methods

Find n-th roots using:

(9) Newton's method [P7.9]
http://en.wikipedia.org/wiki/Newton-Raphson

(10) Bisection method
http://en.wikipedia.org/wiki/Bisection_method

(11) Secant method
http://en.wikipedia.org/wiki/Secant_method

(12) False position method
http://en.wikipedia.org/wiki/False_position_method

(13) Laguerre's method
http://en.wikipedia.org/wiki/Laguerre%27s_method

Methods of Computing Square Roots

(14) Square roots using Newton iteration - Second method
http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Second_method

(15) Finding square roots using mental arithmetic
http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Finding_square_roots_using_mental_arithmetic

Pi Computing Algorithms

(16) Borwein's algorithm
http://en.wikipedia.org/wiki/Borwein%27s_algorithm

(17) Borwein's algorithm (others) - 1. Quadratic convergence, 1987:
http://en.wikipedia.org/wiki/Borwein%27s_algorithm_%28others%29

(18) Borwein's algorithm (others) - 2. Cubical convergence, 1991:
http://en.wikipedia.org/wiki/Borwein%27s_algorithm_%28others%29

(19) Borwein's algorithm (others) - 3. Quartical convergence, 1984:
http://en.wikipedia.org/wiki/Borwein%27s_algorithm_%28others%29

(20) Borwein's algorithm (others) - 4. Quintical convergence:
http://en.wikipedia.org/wiki/Borwein%27s_algorithm_%28others%29