perplexus.info :: Just Math : Inverse Expression Exercise

Inverse Expression Exercise (Posted on 2015-07-07)

(A) Find all possible positive integer solutions to this equation and prove that there are no others:

(1 + 1/P)(1 + 1/Q)(1 + 1/R) (1 + 1/S) (1 + 1/T) = 14.4, with the restriction
P ≤ Q ≤ R ≤ S ≤ T

(B) What is the total number of positive integer solutions to the above equation without the restriction?

No Solution Yet Submitted by K Sengupta

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probabile solution

Comment 1 of 1

(1,1,1,2,5) for (p,q,r,s,t) seems to be the only solution, though I have no proof.

If that's the case, then the total number of solutions without the restriction is the ways of rearranging these numbers: 5*4 = 20.

Posted by Charlie on 2015-07-07 16:50:57

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