Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm trying to determine the ideal class group of $\mathbb{Q}(\sqrt{223})$ using elementary methods.

Is there an easy way to show that $a^2 - 223b^2 = - 3$ has no integer solutions? I've tried reducing mod just about everything I could think of, but that doesn't seem to help. Any suggestions?

share|cite|improve this question
up vote 3 down vote accepted

Go here and put in the equation and click on "step-by-step" and you will get a proof that there are no solutions. Basically, the left side is so small that any solution has to come from the continued fraction for $\sqrt{223}$, but this has a very short period, and $-3$ doesn't show up.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.