please use python or pari$/$gp to solve this assignment. please note I need it as soon as posible. please make sure to provide the full output along with the implementation. Part II: The factorisation

The task is to complete programming the quadratic sieve as described for B for the size of the factor base, and to apply the program to factorise the

numbers n below. Printouts of your program must be included in your submissions for a grade to be

assigned, but grades are dependent solely on your numerical answers.

For each number n listed below do the following.

$1.$ List a set of exponents e$1,$ e$2,...,$ eK$+2$ and a set of xj such that

$($x$2$

$1$ n$)$e$1($x$2$

$2$ n$)$e$2...($x$2$

K$+2$ n$)$eK$+2$

is a perfect square, y$2,$ and

$2.$ such that when x $=$ xe$1$

$1$ xe$2$

$2...$ xeK$+2$

K$+2$ and y is as above gcd$($x $$ y$,$ n$)$ gives a non$-$trivial factori$-$

sation of n$,$

$3.$ and list the values of x$,$ y and gcd$($x $$ y$,$ n$).$

n $=3215031751,$

n $=9912409831,$

n $=37038381852397,$

n $=341550071728321,$

n $=31868712526338419047.$

It should be possible to copy these numbers from this $.$pdf$.$ They can also be copied from my web

site.

Because of a bug in the server you may have to click on that twice.

For several of these numbers it may be necessary to increase the number of B$$factorable numbers

from K $+2$ to maybe K $+8.$ For the last number, if you are using Pari$/$gp you will need to be careful

about memory, the allotment of which can be increased by allocatemem, and it may be necessary to

choose something a little smaller than B$2$ for the initial choice of the number of x to try.