I need to solve the following problem:

"=" means is congruent to.

x^7 = 12 mod 29

This is what I have:

I am using q=2 as the primitive root mod 29.

7*I(x)=I(12) mod 28

7*I(x)=7 mod 28

I(x) = 1 mod 4

What do I do next?

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- Apr 23rd 2010, 03:56 PMsantiagos11x^7 = 12 mod 29 (primitive roots)
I need to solve the following problem:

"=" means is congruent to.

x^7 = 12 mod 29

This is what I have:

I am using q=2 as the primitive root mod 29.

7*I(x)=I(12) mod 28

7*I(x)=7 mod 28

I(x) = 1 mod 4

What do I do next? - Apr 23rd 2010, 07:53 PMsantiagos11
never mind, I got it. i will post the solution later

- Apr 23rd 2010, 07:57 PMchiph588@
Well , so we know .

Therefore

Our solutions are thus .

Note that these are the only solutions since is a primitive root, so generate all possibe solutions.