1: write a program to do the following:

 a.find the gcd of two numbers using eucid's algorithm  .

def gcd(a, b):

    if b == 0:

        return a

    elif b > a:

        return gcd(b, a)

    else:

        return gcd(b, a % b)

B: find the no of integral solution for equation.

#find the no of positive integral for a2-b2=N

from math import sqrt

pf = []

n = int(input("Enter a number: "))

x = n

while n % 2 == 0:

    pf.append(2)

    n = n // 2

i = 3

while i <= sqrt(n):

    while n % i == 0:

        pf.append(i)

        n = n // i

        i = i + 2

if n > 2:

    pf.append(n)

print("Prime factors of", x, "are", pf)

pf1 = set(pf)

nf = 1

for f in pf1:

    cnt = 0

    for f1 in pf:

        if f == f1:

            cnt += 1

    nf *= cnt + 1

print("Number of factors of", x, "=", nf)

print("Number of possible positive integral solutions =", nf // 2)

c: enter  a positive number N and find number a and b such that a2-b2=N

N=36

a=9 #factors of 36

b=4

print("the value of positive number N is :",N)

print("factors of N are",a,b)

x=(a+b)/2

y=(a-b)/2

asqr=x**2

bsqr=y**2

print("the value of a**2 and B**2 :",asqr,bsqr)

N=asqr-bsqr

print("asqr-bsqr=",N)