#### Exercise 85

Write an algorithm in Python which determines the list of all pairs of relative integers (x, y) verifying the equation : xy – x – y = n for a given integer n. give the result for n = 19.

#### Solution

`def solutionsEq(n):`

# Initialize list of solutions

listSolution = []

for x in range(-n , n + 1):

for y in range(-n , n + 1):

if x*y - x - y == 19:

listSolution.append((x,y))

return listSolution

# Testing algorithm

print("List of solutions tuples is : " , solutionsEq(19))

The output is:

List of solutions tuples is : [(-19, 0), (-9, -1), (-4, -3), (-3, -4), (-1, -9), (0, -19), (2, 21), (3, 11), (5, 6), (6, 5), (11, 3), (21, 2)]

**Younes Derfoufi**

my-courses.net

my-courses.net