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%I #30 Sep 08 2022 08:46:14
%S 1,2,3,6,7,9,14,18,19,21,27,29,31,37,38,42,47,53,54,57,58,59,62,63,74,
%T 81,83,87,93,94,103,106,109,111,113,114,118,126,131,133,137,139,141,
%U 149,159,162,166,167,171,174,177,186,189,193,197,199,203,206,217,218,222
%N Numbers k such that 7 is a square mod k.
%H Alois P. Heinz, <a href="/A262932/b262932.txt">Table of n, a(n) for n = 1..20000</a>
%e 7^2 == 7 (mod 14), so 14 is a term.
%e 5^2 == 7 (mod 18) and 13^2 == 7 (mod 18), so 18 is a term.
%p with(numtheory):
%p a:= proc(n) option remember; local k;
%p for k from 1+`if`(n=1, 0, a(n-1))
%p while mroot(7, 2, k)=FAIL do od; k
%p end:
%p seq(a(n), n=1..80); # _Alois P. Heinz_, Feb 24 2017
%t Join[{1}, Table[If[Reduce[x^2 == 7, Modulus->n] === False, Null, n], {n, 2, 300}]//Union] (* _Vincenzo Librandi_, Oct 05 2015 *)
%o (PARI) for(n=1, 300, if (issquare(Mod(7, n)), print1(n", "))); \\ _Altug Alkan_, Oct 04 2015
%o (Magma) [n: n in [1..300] | exists(t){x : x in ResidueClassRing(n) | x^2 eq 7}]; // _Vincenzo Librandi_, Oct 05 2015
%Y Cf. A057125, A057126, A057762, A262931.
%K nonn,easy
%O 1,2
%A _Erik Pelttari_, Oct 04 2015
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