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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. 22

%I

%S 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,

%T 28,11,30,15,10,33,6,17,36,37,14,9,40,13,42,21,19,45,46,7,48,49,16,25,

%U 52,53,21,13,20,57,58,11,60,61,8,31,14,23,66,33,22,29

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

%C 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

%H Alois P. Heinz, <a href="/A070667/b070667.txt">Table of n, a(n) for n = 1..10000</a>

%p a:= proc(n) local k; for k from 2 do if 1=k*k mod n

%p then return k elif k>=n then return 1 fi od

%p end:

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Oct 30 2016

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

%Y Cf. A033948, A033949, A000961.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, May 08 2002

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Last modified November 14 04:56 EST 2019. Contains 329110 sequences. (Running on oeis4.)