--%>
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 : Problem on reduced row-echelon The

    The augmented matrix from a system of linear equations has the following reduced row-echelon form. 280_row echelon method.jpg

    		•
  • Q : Explain Factorisation by trial division

    Factorisation by trial division: The essential idea of factorisation by trial division is straightforward. Let n be a positive integer. We know that n is either prime or has a prime divisor less than or equal to √n. Therefore, if we divide n in

    		•
  • Q : Pig Game Using the PairOfDice class

    Using the PairOfDice class design and implement a class to play a game called Pig. In this game the user competes against the computer. On each turn the player rolls a pair of dice and adds up his or her points. Whoever reaches 100 points first, wins. If a player rolls a 1, he or she loses all point

    		•
  • Q : Nonlinear integer programming problem

    Explain Nonlinear integer programming problem with an example ?

    		•
  • Q : Problem on sales and budget XYZ Farm

    XYZ Farm Supply data regarding the store's operations follow: • Sales are budgeted at $480,000 for November, $430,000 for December, and $340,000 for January. • Collections are expected

    		•
  • Q : Who developed a rigorous theory for

    Who developed a rigorous theory for Brownian motion?

    		•
  • Q : Mathematical Method for Engineers The

     The function is clearly undefined at , but despite all of this the function does have a limit as approaches 0. a) Use MATLAB and ezplot to sketch for , and use the zoom on facility to guess the . You need to include you M-file, outp

    		•
  • Q : Explain lognormal stochastic

    Explain lognormal stochastic differential equation for evolution of an asset.

    		•
  • Q : Statistics math Detailed explanation of

    Detailed explanation of requirements for Part C-1 The assignment states the following requirement for Part 1, which is due at the end of Week 4: “Choose a topic from your field of study. Keep in mind you will need to collect at least [sic] 3- points of data for this project. Construct the sheet y

    		•
  • Q : The mean of the sampling distribution

    1. Caterer determines that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. If P-hat is the proportion saying that the food is delicious, what is the mean of the sampling distribution p-hat?<

    		•