A Quadratic Residues Parlor Trick
D. M. Bloom · Mathematics Magazine · 1998
Statements Choose a prime p > 3 such that p 3 (mod 4), but don't tell me what p is. Now do (or have your computer do) the following calculations: (1) determine which numbers between 0 and p/2 are quadratic residues modulo p (i.e., are congruent to squares, mod p); (2) find the sum of these low quadratic residues; (3) replace said sum by its least non-negative residue r (mod p). Here are three examples: