Determine all possible octuplets (A, B, C, D, E, F, G, H) of positive integers, with A ≤ B ≤ C ≤ D, and, E ≤ F ≤ G ≤ H and, A ≤ E, that satisfy both the equations: A+B+C+D = E*F*G*H and, A*B*C*D = E+F+G+H.
Prove that these are the only octuplets that exist.
Like ed bottemiller I had some doubt as to if the equations were to be considered together or whether they could stand alone.
If the equations are to be considered together then:
A,B,C,D are 1,1,2,4 as are E,F,G,H in the same order.
If the equations may stand alone then
A B C D E F G H
1 1 1 9 1 1 3 4 or
this also holds true
1 1 3 4 1 1 1 9
Posted by brianjn
on 2010-03-04 20:09:57