Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

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

The proof and various concrete examples make the lemma and application clear.

I was wondering if there is an intuitive (or other) perspective so that if you knew the number of negative least residues $\pmod p$ of $a$, $2a$,...$((p - 1)/2)a$, you would know whether $a$ is a quadratic or non-quadratic residue $\pmod p$. Where $a\in \mathbb{Z}$, $p$ an odd prime, and $p$ does not divide $a$.


share|cite|improve this question

Your Answer


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

Browse other questions tagged or ask your own question.