#### Exercise 70

Write an Python algorithm which asks the user to type a **coprime intgeger n and m** and returns a **tuple (u, v)** verifying:** um + vn = 1** (**Bezout identity**)

#### Solution

`# Enter the values of the integers m and n`

m = int (input ("Enter the value of the enier m:"))

n = int (input ("Enter the value of the integer n:"))

# Initialize the value of v to 1

v = 1

# We look for the integer v such that 1-vn is a multiple of n

# while 1-vn is not a multiple of m, we increment the integer v

while (( v*n - 1 )%m != 0):

v = v + 1

# Now the equality um + vn = 1 means that

u = int ((1- v*n)/m)

print ("The tuple that verifies um + vn = 1 is:", (u, v))

**Younes Derfoufi**

my-courses.net

my-courses.net