representants of quadratic residues
constitute a representant system of incongruent quadratic residues modulo . Accordingly, there are quadratic residues and equally many nonresidues modulo .
Proof. Firstly, the numbers (1), being squares, are quadratic residues modulo . Secondly, they are incongruent, because a congruence would imply
which is impossible when and are different integers among . Third, if is any quadratic residue modulo , and therefore the congruence has a solution , then is congruent with one of the numbers
which form a reduced residue system modulo (see absolutely least remainders). Then and are congruent with one of the numbers (1).
|Title||representants of quadratic residues|
|Date of creation||2013-03-22 19:00:35|
|Last modified on||2013-03-22 19:00:35|
|Last modified by||pahio (2872)|
|Synonym||representant system of quadratic residues|