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My favorite numbers II (Posted on 2009-12-21)

Determine all possible sextuplets (A, B, C, D, E, F) of positive integers, with A ≤ B ≤ C, and, D ≤ E ≤ F and, A ≤ D, that satisfy both the equations: A+B+C = D*E*F and, A*B*C = D+E+F.

Prove that these are the only sextuplets that exist.

Submitted by K Sengupta

Rating: 4.0000 (1 votes)

Solution: (Hide)

The required sextuplets are:
(1,1,6,1,2,3) (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)
For an explanation, refer to the solution submitted by Dej Mar in this
Comments: ( You must be logged in to post comments.)

Subject Author Date

The start of a proof... Steve Herman 2009-12-23 10:20:36

An attempt at a proof... Dej Mar 2009-12-22 19:28:57

Same result with a listing. brianjn 2009-12-21 19:32:54

Six Sexy-tuplet Solutions Jim Keneipp 2009-12-21 16:56:53

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