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.

(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**