perplexus.info :: Numbers : Reciprocal Equation #8

Reciprocal Equation #8 (Posted on 2023-06-11)

Find all possible triplets (x, y, z) of positive integers that satisfy this equation:

(1+1/x)*(1+1/y)*(1+1/z) = 5

Prove that these are the only possible triplets in conformity with the given conditions.

Note: Computer program solutions are welcome, but an analytic solution is preferred.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(x,y,z)=(1,1,4), (1,4,1) and (4,1,1)
For an explanation, refer to the analytical solution submitted by Steve Herman in this location.

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

Subject	Author	Date
Analytic and Computer solutions	Larry	2023-06-11 20:06:40
Analytic solution	FrankM	2023-06-11 12:07:34
solution	Charlie	2023-06-11 09:37:04
Analytical Spoiler	Steve Herman	2023-06-11 07:52:16

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