Why Does a Solution Exist for the Congruence Equation 59x + 15 ≡ 6 mod n?

[viviane363]

Homework Statement

Let n be a positive integer. Consider the congruence equation 59x + 15 congruent to 6 mod n
For this equation, a solution x exits. Why?

Homework Equations

The Attempt at a Solution

there is a k such that
(59x +15) - 6 = kn
(59x +15) - kn = 6
59x - kn = 6 - 15
59x - kn = -9
there is a linear combination of 59 and k that gives -9
But then, I don't know if this is the right way to go and what to do now!
Thanks to help

 

[Dick]

If n=59 there is no solution. You have to know something about n to decide whether there is a solution.