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My favorite numbers III (Posted on 2010-03-04) Difficulty: 4 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts No Subject | Comment 1 of 6

1+1+2+4=1*1*2*4   looks ok

So far do not see any others.

  Posted by Ady TZIDON on 2010-03-04 11:57:22
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