Numbers n such that x^2 + y^2 (mod n) assumes every number in Zn, where x and y are nonzero.
10, 13, 17, 25, 26, 29, 30, 34, 37, 39, 41, 50, 51, 53, 58, 61, 65, 70, 73, 74, 75, 78, 82, 85, 87, 89, 91, 97, 101, 102, 106, 109, 110, 111, 113, 119, 122, 123, 125, 130, 137, 143, 145, 146, 149, 150, 157, 159, 169, 170, 173, 174, 175, 178, 181, 182, 183, 185, 187, 190, 193, 194, 195, 197
1
T. D. Noe, Plot of terms up to 1000
T. D. Noe, Table of terms up to 1000
Joshua Harrington, Lenny Jones, and Alicia Lamarche, Representing integers as the sum of two squares in the ring Z_n, J. of Integer Seqs. 17 (2014), Article. 14.7.4.
(Mma) nn = 200; t = {}; Do[s = Flatten[Table[Mod[x^2 + y^2, n], {x, n-1}, {y, x, n-1}]]; s = Union[s]; If[Length[s] < n, AppendTo[t, n]], {n, nn}]; t
Cf. A240109 (very similar), S000094 (complement).
nonn
T. D. Noe, Jun 23 2014