editing

approved

Number of distinct solutions of sumSum_{i=1..2}(x(2i-1)*x(2i)) = 0 (mod n), with x() only in 2..n-2.

Column 2 of A180823.

Cf. A180823.

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editing

_R. H. Hardin (rhhardin(AT)att.net) _ Sep 20 2010

R. H. Hardin, <a href="/A180814/b180814.txt">Table of n, a(n) for n=1..999</a>

nonn,new

nonn

Number of distinct solutions of sum{i=1..2}(x(2i-1)*x(2i)) = 0 (mod n), with x() only in 2..n-2

0, 0, 0, 1, 2, 6, 8, 27, 30, 59, 64, 147, 128, 212, 265, 380, 347, 623, 512, 897, 882, 1074, 1000, 1863, 1437, 1907, 2100, 2767, 2204, 3916, 2744, 4255, 4080, 4655, 4783, 7374, 4922, 6686, 7059, 9691, 6869, 11610, 8000, 12011, 12697, 12396, 10648, 18978, 13031

1,5

Column 2 of A180823

R. H. Hardin, <a href="b180814.txt">Table of n, a(n) for n=1..999</a>

Solutions for sum of products of 2 2..6 pairs = 0 (mod 8) are

(2*2 + 2*2) (2*2 + 2*6) (2*2 + 3*4) (2*2 + 4*5) (2*2 + 6*6) (2*3 + 2*5)

(2*3 + 3*6) (2*4 + 2*4) (2*4 + 4*4) (2*4 + 4*6) (2*5 + 5*6) (2*6 + 2*6)

(2*6 + 3*4) (2*6 + 4*5) (2*6 + 6*6) (3*3 + 3*5) (3*4 + 3*4) (3*4 + 4*5)

(3*4 + 6*6) (3*5 + 5*5) (3*6 + 5*6) (4*4 + 4*4) (4*4 + 4*6) (4*5 + 4*5)

(4*5 + 6*6) (4*6 + 4*6) (6*6 + 6*6)

nonn,new

R. H. Hardin (rhhardin(AT)att.net) Sep 20 2010

approved