# Solution Exercise 758: algorithm python to find list of all tuples of integers satisfying some conditions

Sep 17, 2020

#### Exercise 758

Write a python algorithm as a function that takes as argument a pair of integers (d, s) and returns a list of all the couple who determine the list of all pairs of integers (m, n) of greatest common divisor GCD(m, n) = d and of sum m + n = s    (*)

#### Solution

``# Creating a functon which calculating the gcd of two integers.def gcd(m , n):    # initializing the gcd of m and n    d = m    while( m%d != 0 or n%d != 0):        d = d - 1    return d# creating a function that solve th problem (*)def tuplesSolutions(d , s):    # initializing the list of tuples solutions    listTuples = []    for m in range(1 , s ):        for n in range(1 ,s):            if gcd(m , n) == d and m + n == s:                listTuples.append((m,n))    return listTuples# Testing algorithmprint("List of tuples (m,n) such that m + n = 140 et gcd(m,n) = 7 is : n" , tuplesSolutions(7 , 140))"""The output is :List of tuples (m,n) such that m + n = 140 et gcd(m,n) = 7 is :  [(7, 133), (21, 119), (49, 91), (63, 77), (77, 63), (91, 49), (119, 21), (133, 7)]"""``

Younes Derfoufi
my-courses.net