How to Solve a Modular Arithmetic Equation

viviane363
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Homework Statement



compute 59x +15 \equiv 6 mod 811

Homework Equations





The Attempt at a Solution



59x \equiv -9 mod 811
I really don't know hoow to do from here.
 
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so i think 2 numbers a,b are equivalent in modular arthimetic, mod n, if

a-b = m*n for some integer m

in your case this translates to
59x+9 = 811.m
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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