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%I #11 Nov 14 2014 10:37:13
%S 1,1,1,3,3,1,1,3,6,3,11,3,1,1,3,10,1,6,19,11,1,11,1,3,15,1,6,3,29,3,
%T 31,10,11,1,3,21,1,19,1,11,41,1,1,43,24,1,1,10,28,15,1,3,1,6,53,3,19,
%U 29,59,11,61,31,6,36,3,11,1,3,1,3,71,21,1,1,15,75,11,1,79,42,45,41,1,3,3,1,29,43,89,24,1,3,31,1,93,10,1,28,96,55,101,1,1,3,3
%N Number of pairs of integers i,j with 1<=i<=n, 1<=j<=i, such that i^2-j^2 = i*j (mod n).
%C It appears that, except for the first term, a(n)=n if and only if n is a prime congruent to 1 or 4 (mod 5).
%H Alois P. Heinz, <a href="/A197928/b197928.txt">Table of n, a(n) for n = 1..1000</a>
%p a:= n-> add(add(`if`(irem((i-j)*(i+j)-i*j, n)=0, 1, 0), j=1..i), i=1..n):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Oct 19 2011
%Y Cf. A180783.
%K nonn
%O 1,4
%A _John W. Layman_, Oct 19 2011
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