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%I #37 Dec 18 2023 13:57:43
%S 0,1,4,9,16,6,17,11,7,5,5,7,11,17,6,16,9,4,1,0,1,4,9,16,6,17,11,7,5,5,
%T 7,11,17,6,16,9,4,1,0,1,4,9,16,6,17,11,7,5,5,7,11,17,6,16,9,4,1,0,1,4,
%U 9,16,6,17,11,7,5,5,7,11,17,6,16,9,4,1,0,1,4,9,16,6,17,11,7,5,5,7,11
%N n^2 mod 19.
%C x^2 - k = 19*y, where x, y and k are integers, has solutions if and only if k mod 19 is an element of {0,1,4,5,6,7,9,11,16,17}. - _Vincenzo Librandi_, Aug 12 2014
%H Vincenzo Librandi, <a href="/A070441/b070441.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F a(n+19) = a(n).
%F a(19*k - n) = a(n). - _Robert Israel_, Aug 12 2014
%p A070441:=n->n^2 mod 19: seq(A070441(n), n=0..100); # _Wesley Ivan Hurt_, Aug 12 2014
%t Table[Mod[n^2,19],{n,0,200}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 23 2011 *)
%t PowerMod[Range[0,90],2,19] (* _Harvey P. Dale_, Mar 23 2012 *)
%o (Magma) [n^2 mod(19): n in [0..100]]; // _Vincenzo Librandi_, Aug 12 2014
%o (PARI) a(n)=n^2%19 \\ _Charles R Greathouse IV_, Apr 06 2016
%Y Cf. A070442, A070443, A070444.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 12 2002