--%>
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 : Ordinary Differential Equation or ODE

    What is an Ordinary Differential Equation (ODE)?

    		•
  • Q : Area Functions & Theorem Area Functions

    Area Functions 1. (a) Draw the line y = 2t + 1 and use geometry to find the area under this line, above the t - axis, and between the vertical lines t = 1 and t = 3. (b) If x > 1, let A(x) be the area of the region that lies under the line y = 2t + 1 between t

    		•
  • Q : Numerical Analysis Hi, I was wondering

    Hi, I was wondering if there is anyone who can perform numerical analysis and write a code when required. Thanks

    		•
  • Q : Theorem-G satis es the right and left

    Let G be a group. (i) G satis es the right and left cancellation laws; that is, if a; b; x ≡ G, then ax = bx and xa = xb each imply that a = b. (ii) If g ≡ G, then (g-1)

    		•
  • 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

    		•
  • Q : Mathematical and Theoretical Biology

    Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in the fields of biology, biotechnology, and medicine. The field may be referred to as mathematical biology or biomathematics to stress the mathematical

    		•
  • Q : Global And Regional Economic Development

    The Pharmatec Group, a supplier of pharmaceutical equipment, systems and services, has its head office in London and primary production facilities in the US. The company also has a successful subsidiary in South Africa, which was established in 1990. Pharmatec South A

    		•
  • Q : Problem on Linear equations Anny, Betti

    Anny, Betti and Karol went to their local produce store to bpought some fruit. Anny bought 1 pound of apples and 2 pounds of bananas and paid $2.11.  Betti bought 2 pounds of apples and 1 pound of grapes and paid $4.06.  Karol bought 1 pound of bananas and 2

    		•
  • Q : Properties for polynomial Specify the

    Specify the important properties for the polynomial.

    		•
  • Q : Who firstly use the finite-difference

    Who firstly use the finite-difference method?

    		•