--%>
Assignment Help - homework help

State Fermat algorithm

The basic Fermat algorithm is as follows:

Assume that n is an odd positive integer. Set c = [√n] (`ceiling of √n '). Then we consider in turn the numbers

c2 - n; (c+1)2 - n; (c+2)2 - n.....

until a perfect square is found. If this occurs at the term (c+k)2 - n, then putting a = c+k we have

a2 - n = (c+k)2 - n = b2;

say, and then n = a2 - b2, as desired.

This process will terminate in the worst case when a = (n+1)/2, since

n = [(n+1)/2]2 - [(n-1)/2]2
 
In particular, the number of steps taken will be at worst

(n+1)/2 - [√n] +1 = O(n)

   Related Questions in Mathematics

  • Q : Who derived the Black–Scholes Equation

    Who derived the Black–Scholes Equation?

    		•
  • Q : Competitive equilibrium 8. Halloween is

    8. Halloween is an old American tradition. Kids go out dressed in costume and neighbors give them candy when they come to the door. Spike and Cinderella are brother and sister. After a long night collecting candy, they sit down as examine what they have. Spike fi

    		•
  • Q : Who firstly use the finite-difference

    Who firstly use the finite-difference method?

    		•
  • Q : Probability assignments 1. Smith keeps

    1. Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20substandard? 2. Realtors estimate that 23% of homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2

    		•
  • Q : Explain Factorisation by Fermats method

    Factorisation by Fermat's method: This method, dating from 1643, depends on a simple and standard algebraic identity. Fermat's observation is that if we wish to nd two factors of n, it is enough if we can express n as the di fference of two squares.

    		•
  • Q : Who had find Monte Carlo and finite

    Who had find Monte Carlo and finite differences of the binomial model?

    		•
  • Q : Who developed a rigorous theory for

    Who developed a rigorous theory for Brownian motion?

    		•
  • Q : First-order formulas over the

    Consider the unary relational symbols P and L, and the binary relational symbol On, where P(a) and I(a) encode that a is apoint and a (sraight) line in the 2-dimensional space, respectively, while On(a,b) encodes  that a is a point, b is a line, and o lies on b.

    		•
  • Q : Problem on Nash equilibrium In a

    In a project, employee and boss are working altogether. The employee can be sincere or insincere, and the Boss can either reward or penalize. The employee gets no benefit for being sincere but gets utility for being insincere (30), for getting rewarded (10) and for be

    		•
  • Q : Formal logic It's a problem set, they

    It's a problem set, they are attached. it's related to Sider's book which is "Logic to philosophy" I attached the book too. I need it on feb22 but feb23 still work

    		•