## Cryptology and Congruence

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. 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
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 Recognitions: Homework Help Science Advisor If n=59 there is no solution. You have to know something about n to decide whether there is a solution.

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