--%>
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 : Solve each equation by factoring A

    A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%.  If his annual interest is $1,670 how much did he invest at 6%?  If I told you the answer is $8,000, in your own words, using complete sentences, explain how you

    		•
  • Q : Research Areas in Medical Mathematical

    Some Research Areas in Medical Mathematical Modelling:1. Modeling and numerical simulations of the nanometric aerosols in the lower portion of the bronchial tree. 2. Multiscale mathematical modeling of

    		•
  • 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 : Maths assignment complete assignment

    complete assignment with clear solution and explanation

    		•
  • Q : Bolzano-Weierstrass property The

    The Bolzano-Weierstrass property does not hold in C[0, ¶] for the infinite set A ={sinnx:n<N} : A is infinite; Show that has no “ limit points”.

    		•
  • Q : State Fermat algorithm The basic Fermat

    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 th

    		•
  • Q : Problem on augmented matrix Consider

    Consider the following system of linear equations.  (a) Write out t

    		•
  • Q : What is Big-O hierarchy The big-O

    The big-O hierarchy: A few basic facts about the big-O behaviour of some familiar functions are very important. Let p(n) be a polynomial in n (of any degree). Then logbn is O(p(n)) and p(n) is O(an<

    		•
  • Q : Define Big-O notation Big-O notation :

    Big-O notation: If f(n) and g(n) are functions of a natural number n, we write f(n) is O(g(n)) and we say f is big-O of g if there is a constant C (independent of n) such that f

    		•
  • Q : Explain trading of call options Explain

    Explain trading of call options.

    		•