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%I #19 Dec 20 2021 08:00:06
%S 2,3,6,7,13,14,17,21,23,26,34,37,39,42,43,46,47,51,53,67,69,73,74,78,
%T 83,86,91,94,97,102,103,106,107,111,113,119,127,129,134,137,138,141,
%U 146,157,159,161,163,166,167,173,182,193,194,197,201,206,214,219
%N Positive integers k such that there is no solution of the equation x^2 + y^2 + 3*x*y = 0 in Z/nZ except for the trivial one (0,0).
%C Prime numbers of this sequence are congruent to {2,3} modulo 5.
%e The only solution of the equation x^2 + y^2 + 3*x*y = 0 in Z/2Z is (0,0).
%e 4 is not in the sequence because 0^2 + 2^2 + 3*2*0 = 4 == 0 (mod 4). 5 is not in the sequence because 1^2 + 1^2 + 3*1*1 = 5 == 0 (mod 5). 10 is not in the sequence because 2^2 + 2^2 + 3*2*2 = 20 == 0 (mod 10). - _R. J. Mathar_, Jun 16 2019
%p isA167415 := proc(n)
%p local x,y ;
%p for x from 0 to n-1 do
%p for y from x to n-1 do
%p if modp(x^2+y^2+3*x*y,n) = 0 and (x <> 0 or y <> 0) then
%p return false;
%p end if;
%p end do:
%p end do:
%p true ;
%p end proc:
%p for n from 2 to 300 do
%p if isA167415(n) then
%p printf("%d,",n) ;
%p end if;
%p end do: # _R. J. Mathar_, Jun 16 2019
%Y Cf. A031363 (x^2 + y^2 + 3xy).
%K easy,nonn
%O 1,1
%A _Arnaud Vernier_, Nov 03 2009
%E Name corrected by _R. J. Mathar_, Jun 16 2019 and Don Reble
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