Thread: Solving for x in a quadratic congruence modulo problem

So our class was given this to look over before our last class before the break:

I got a value that works,
but not sure if this is the only answer and I went about it probably not in the correct fashion.

What I did was just notice that , then I though that if , then , and it turns out that as well.
I doubt you can just eliminate terms like this to make it work.

All the examples I've read here don't deal with anything more than say or whatever. So I wasn't sure how to approach when a whole quadratic equation was on the LHS.
Also, the quadratic formula doesn't give any real solutions, so my original theory of using that doesn't work.

Any help would be appreciated, Thanks.

since

So we want

Since 5 is coprime to 11 it must be that

Now, since 11 is prime, it follows that it divides the product if and only if it divides one of the 2 factors.

So the solutions are: and

Oh, so we're not solving for particular values of x?

Think I understand everything except for what the co-prime means, don't think we've covered it yet.

Thanks, though, now I can go into class knowing a bit more about what to do.

Originally Posted by Th3sandm4n

Think I understand everything except for what the co-prime means, don't think we've covered it yet.

It just means if and then . If we did not know that we cannot conclude anything further, as the next example illustrate. Let and notice that however, .