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A180784 Number of distinct solutions of sum{i=1..2}(x(2i-1)*x(2i)) = 1 (mod n), with x() only in 1..n-1.

%I A180784 #5 Jun 02 2025 03:05:16
%S A180784 0,0,1,4,9,19,31,42,75,91,136,160,232,254,364,388,542,525,767,754,
%T A180784 1015,993,1389,1256,1795,1641,2169,2080,2838,2344,3484,3144,3971,3676,
%U A180784 4980,4152,5989,5135,6564,6008,8195,6392,9476,8064,9912,9114,12426,9808,14032
%N A180784 Number of distinct solutions of sum{i=1..2}(x(2i-1)*x(2i)) = 1 (mod n), with x() only in 1..n-1.
%C A180784 Column 2 of A180793
%H A180784 R. H. Hardin, <a href="/A180784/b180784.txt">Table of n, a(n) for n=1..999</a>
%e A180784 Solutions for sum of products of 2 1..5 pairs = 1 (mod 6) are
%e A180784 (1*1 + 2*3) (1*1 + 3*4) (1*2 + 1*5) (1*3 + 1*4) (1*3 + 2*2) (1*3 + 2*5)
%e A180784 (1*3 + 4*4) (1*4 + 3*3) (1*4 + 3*5) (1*5 + 2*4) (1*5 + 4*5) (2*2 + 3*3)
%e A180784 (2*2 + 3*5) (2*3 + 5*5) (2*5 + 3*3) (2*5 + 3*5) (3*3 + 4*4) (3*4 + 5*5)
%e A180784 (3*5 + 4*4)
%K A180784 nonn
%O A180784 1,4
%A A180784 _R. H. Hardin_ Sep 20 2010