How to solve equation with div without iterating?

Question

Python

There is an equation like:
x - 4(x div 7) = 7
You need to find the minimum value of x. Preferably without busting, tk. 1 <= x <= 2*10^9

Answer 1

If 4 and 7 in the example are two parameters of the equation (a and b, respectively), taking only positive integer values, then without enumeration - easily:

def solve_equation(a,b):   # x - a(x div b) = b
    if a%1 + b%1 != 0:
        raise ValueError('both variables must have integer values')
    if 0 < a < b: x = a + b
    else: x = None
    return x

In the sense that for any a < b the answer is: a + b. For all others, there is no solution.