Write a Python code, please. Two integers are relatively prime if they have no common divisors other than $1.$ An equation in the form ax $+$ by $=1$ has an integer solution if and only if a and b are relatively prime. For example, if a $=8$ and b $=21,$ then integer solutions exist for x and y in the equation $8$x $+21$y $=1.$ The solutions can be found by reducing the coefficients and back$-$substituting.

Refer to "Linear Diophantine Equations," located in the topic Resources, and write a Python function that implements this concept. The function will have a and b as input to find GCD$($a$,$b$)$ and check if they are relatively prime. If they are relatively prime, it calculates x and y and prints ax $+$ by $=1,$ and if not, it will print a and b and GCD$($a$,$b$).$

Next, write a program that generates $20$ pairs of positive random integers in the range $[1,9999].$ For each pair generated, call your function to print the result.