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.
I don't think this problem is that simple. The first question is whether "integer" is limited to "digits", or does it include any whole numbers. It is not required that the same numbers of used.
Consider (1,1,1,9) and (1,1,3,4):