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Determine all possible sextuplets (P, Q, R, S, T, U) of positive integers, with P ≤ Q ≤ R, and S ≤ T ≤ U, satisfying both of the following conditions:

P+Q+R = S*T*U and, P*Q*R = S+T+U.

Edited September 29, 2009 by K Sengupta

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I'll go ahead and give the obvious ones...

(0,0,0,0,0,0) and (1,2,3,1,2,3)

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missed the positive int part

Edited September 29, 2009 by mordimar

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(1,1,8,1,2,5)

(1,1,7,1,3,3)

(1,1,6,2,2,2)

Edited September 29, 2009 by ljb

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(1,1,6,2,2,2) (1,1,7,1,3,3) (1,1,8,1,2,5) (1,2,3,1,2,3) (1,2,5,1,1,8) (1,3,3,1,1,7) (2,2,2,1,1,6)