perplexus.info :: Just Math : Modified Product = Sum

Modified Product = Sum (Posted on 2010-05-24)

Determine all possible quintuplet(s) (A,B,C,D,E) of positive integers, with A ≤ B ≤ C ≤ D ≤ E, that satisfy this equation:

(A-1)*(B-2)*(C-3)*(D-4)*(E-5) = A+B+C+D+E

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

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

A B C D E LHS RHS 2 3 4 6 25 40 40 2 3 5 5 25 40 40 2 3 5 6 12 28 28 2 4 4 5 25 40 40 2 4 4 6 12 28 28 2 4 5 5 12 28 28 3 3 4 5 25 40 40 3 3 4 6 12 28 28 3 3 5 5 12 28 28 3 4 4 5 12 28 28
For an explanation, refer to the solution submitted by Charlie in this location.
You can also refer to the analytic solution posited by Ady TZIDON in this location.

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

Subject	Author	Date
a solution , speadsheet aided	Ady TZIDON	2010-05-24 14:09:34
computer solution + proof	Charlie	2010-05-24 13:44:42

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