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A070667
Smallest m in range 2..n-1 such that m^2 == 1 mod n, or 1 if no such number exists.
23
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
1,3
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)<n-1. E.g.: if n is of the form 4*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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 08 2002
STATUS
approved