

A316976


Numbers n such that some of the values (r0r1+n) mod n for all pairs (r0,r1) of quadratic residues mod n are unique.


0



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
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OFFSET

1,2


COMMENTS

These are the numbers n such that A316975(n) = 1.
It is conjectured that this list is finite and limited to the terms given in the DATA section.
All known terms are 5smooth.


LINKS

Table of n, a(n) for n=1..42.


EXAMPLE

The quadratic residues mod 12 are 0, 1, 4 and 9. For each pair (r0,r1) of these quadratic residues, we compute (r0r1+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.


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 *)


CROSSREFS

Cf. A096008, A316975, A051037.
Sequence in context: A217288 A212011 A207005 * A256173 A050070 A050590
Adjacent sequences: A316973 A316974 A316975 * A316977 A316978 A316979


KEYWORD

nonn


AUTHOR

Arnauld Chevallier, Jul 17 2018


STATUS

approved



