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%I #3 Mar 30 2012 17:27:41
%S 34,52,60,63,80,70,52,92,51,52,126,148,155,156,76,94,220,250,110,174,
%T 240,200,187,182,191,192,190,266,278,328,320,322,203,98,250,395,243,
%U 242,160,300,308,432,160,390,345,338,349,410,420,266,157,153,395,121,490
%N Second component of quadruples a,b,c,d such that a < b < c < d, (a*b*c) mod (a+b+c) = d, (a*b*d) mod (a+b+d) = c, (a*c*d) mod (a+c+d) = b, (b*c*d) mod (b+c+d) = a. The quadruples are ordered according to sum of first three components, secondary by first component, thirdly by second component.
%C Suggested by Thomas A. Nagy. - A092887 gives first component, A092889 gives third component, A092890 gives fourth component.
%e The fifth quadruple is 48, 80, 96, 160, hence a(5) = 80.
%o (PARI) {m=1140;for(n=6,m, for(a=1,(n-3)\3, for(b=a+1,(n-a-1)\2,c=n-a-b;d=a*b*c%(a+b+c); if(c<d,if(a*b*d%(a+b+d)==c,if(a*c*d%(a+c+d)==b,if(b*c*d%(b+c+d)==a,print1(b,","))))))))}
%Y Cf. A092887, A092889, A092890, A092891.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Mar 12 2004
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