A316976 Numbers k such that some of the values (r0-r1+k) mod k for all pairs (r0,r1) of quadratic residues mod k are unique.
1, 3, 4, 5, 8, 9, 12, 15, 16, 20, 24, 32, 36, 40, 45, 48, 60, 64, 72, 80, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760
Offset: 1
Keywords
Examples
The quadratic residues mod 12 are 0, 1, 4 and 9. For each pair (r0,r1) of these quadratic residues, we compute (r0-r1+12) mod 12, leading to:
0 1 4 9
+------------
0 | 0 11 8 3
1 | 1 0 9 4
4 | 4 3 0 7
9 | 9 8 5 0
The values 1, 5, 7 and 11 are unique in the above table. Therefore 12 belongs to the list.
Programs
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Mathematica
Select[Range[10^3], Function[{n}, Min@ Tally[#][[All, -1]] == 1 &@ Flatten[Mod[#, n] & /@ Outer[Subtract, #, #]] &@ Union@ PowerMod[Range@ n, 2, n]]] (* Michael De Vlieger, Jul 20 2018 *)
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