#### Exercise 514

Write an algorithm in Python which determines the list of pairs of integers (m, n) satisfying:

- GCD (2m – 1, 2n + 1) = 3
- 0 < m < 100 and 0 < n < 100

#### Solution

`def gcd (m , n):`

d = m

while(m%d !=0 or n%d !=0):

d = d - 1

return d

listSolutions = []

for m in range(1 , 100):

for n in range(1, 100):

if gcd(2*m-1, 2*n+1) == 3:

listSolutions.append((m , n))

print(listSolutions)

**Younes Derfoufi**

my-courses.net

my-courses.net