A070667 Smallest m in range 2..n-1 such that m^2 == 1 mod n, or 1 if no such number exists.

1, 1, 2, 3, 4, 5, 6, 3, 8, 9, 10, 5, 12, 13, 4, 7, 16, 17, 18, 9, 8, 21, 22, 5, 24, 25, 26, 13, 28, 11, 30, 15, 10, 33, 6, 17, 36, 37, 14, 9, 40, 13, 42, 21, 19, 45, 46, 7, 48, 49, 16, 25, 52, 53, 21, 13, 20, 57, 58, 11, 60, 61, 8, 31, 14, 23, 66, 33, 22, 29

Offset: 1

Author

N. J. A. Sloane, May 08 2002

Keywords

• nonn

Comments

If n has a primitive root (i.e. if n is in A033948(n)) then a(n)=n-1, if not (i.e. if n is in A033949(n)), a(n)A000961(m), then a(n)=n/2-1. Questions : for which n does the equation A070667(x)=x-n have at least one solution, does always A070667(x)=x-p have at least one solution when p is prime =>5? - Benoit Cloitre, May 12 2002

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033948, A033949, A000961.

Programs

Maple

a:= proc(n) local k; for k from 2 do if 1=k*k mod n
      then return k elif k>=n then return 1 fi od
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 30 2016

Mathematica

Join[{1,1},Flatten[Table[Select[Range[2,n-1],PowerMod[#,2,n]==1&,1],{n,70}]]] (* Harvey P. Dale, May 01 2012 *)