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A167415 Positive integers n 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). 0
2, 3, 6, 7, 13, 14, 17, 21, 23, 26, 34, 37, 39, 42, 43, 46, 47, 51, 53, 67, 69, 73, 74, 78, 83, 86, 91, 94, 97, 102, 103, 106, 107, 111, 113, 119, 127, 129, 134, 137, 138, 141, 146, 157, 159, 161, 163, 166, 167, 173, 182, 193, 194, 197, 201, 206, 214, 219 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime numbers of this sequence are congruent to {2,3} modulo 5.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

The only solution of the equation x^2 +y^2 +3*x*y = 0 in Z/2Z is (0,0).

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 sequence because 2^2+2^2+3*2*2= 20 == 0 (mod 10). - R. J. Mathar, Jun 16 2019

MAPLE

isA167415 := proc(n)

    local x, y ;

    for x from 0 to n-1 do

        for y from x to n-1 do

            if modp(x^2+y^2+3*x*y, n) = 0 and ( x <>0 or y <> 0) then

                return false;

            end if;

        end do:

    end do:

    true ;

end proc:

for n from 2 to 300 do

    if isA167415(n) then

        printf("%d, ", n) ;

    end if;

end do: # R. J. Mathar, Jun 16 2019

CROSSREFS

Cf. A031363 (x^2+y^2+3xy)

Sequence in context: A073712 A157200 A255940 * A018511 A182708 A304709

Adjacent sequences:  A167412 A167413 A167414 * A167416 A167417 A167418

KEYWORD

easy,nonn

AUTHOR

Arnaud Vernier, Nov 03 2009

EXTENSIONS

NAME corrected. - R. J. Mathar, Jun 16 2019 and Don Reble.

STATUS

approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)