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%I #3 Mar 30 2012 17:27:41
%S 40,97,128,88,96,142,151,164,238,237,189,184,174,212,304,295,268,256,
%T 350,279,350,320,374,308,443,328,475,329,290,394,416,367,470,686,517,
%U 438,585,605,640,620,572,498,736,455,435,650,502,635,625,605,846,891
%N Third 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, A092888 gives second component, A092890 gives fourth component.
%e The fourth quadruple is 56, 63, 88, 171, hence a(4) = 88.
%o (PARI) {m=1110;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(c,","))))))))}
%Y Cf. A092887, A092888, A092890, A092891.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Mar 12 2004