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My favorite numbers III (Posted on 2010-03-04)

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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

There are five octuplets that satisfy both equations:
1.( 1, 1, 1, 9, 1, 1, 3, 4) 2.( 1, 1, 1,11, 1, 1, 2, 7) 3.( 1, 1, 2, 4, 1, 1, 2, 4) 4.( 1, 1, 2, 7, 1, 1, 1,11) 5.( 1, 1, 3, 4, 1, 1, 1, 9)
No one has furnished any proof.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
solution without proof	Dej Mar	2010-03-04 21:51:56
re: Mutually inclusive	ed bottemiller	2010-03-04 20:32:51
Mutually inclusive	brianjn	2010-03-04 20:09:57
re: As simple as possible, but no simpler...	ed bottemiller	2010-03-04 17:51:18
As simple as possible, but no simpler...	ed bottemiller	2010-03-04 17:43:30
No Subject	Ady TZIDON	2010-03-04 11:57:22

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