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My favorite numbers VI (Posted on 2010-11-21) Difficulty: 4 of 5
Determine all possible sextuplet(s) (A, B, C, D, E, F), with B < C, E < F and, A < D, that satisfy this system of equations:

A/(B*C) = D - E - F, and:

D/(E*F) = A - B - C

Prove that these are the only sextuplet(s) that exist.

No Solution Yet Submitted by K Sengupta    
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re: Really? | Comment 2 of 6 |
(In reply to Really? by Steve Herman)

The intended problem text was:

"Determine all possible sextuplet(s) (A, B, C, D, E, F) of positive integers, with B < C, E < F and, A < D, that satisfy this system of equations:

A/(B*C) = D - E - F, and:

D/(E*F) = A - B - C

Prove that these are the only sextuplet(s) that exist."

I don't know how I missed including the "positive integer" part while the problem was on the queue.

Edited on November 21, 2010, 11:12 pm
  Posted by K Sengupta on 2010-11-21 23:09:37

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