Question

For context this should be written in Python and I am looking for a unique solution, not one copied from elsewhere online.

If the gcd(a,b) = 1, we say a and b are relatively prime. For any two relatively prime integers, there exist integers x and y such that ax + by = 1. This is called an example of a Linear Diophantine equation. Write a program that finds this x and y for each relatively prime pair.

Answer 1

• There is a module named diophantine in sympy package, specifically desgined to solve Linear diophantine equaitons.
• diophantine equations have more than one solution. we can use base_solution_linear to get the principal soltuion

program

from sympy import symbols
from sympy.solvers.diophantine.diophantine import base_solution_linear

a = int(input("a = "))
b = int(input("b = "))

#solution for a*x + b*y = 1
sol = base_solution_linear(1, a, b,)
print(f"x = {sol[0]}\ny = {sol[1]}")

sample input and output:

la 17 b = 9 X = -1 ay = 2