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Product Divides Sum? (Posted on 2015-05-12) Difficulty: 2 of 5
Each of P, Q and R is a positive integer such that P divides Q2, Q divides R2 and R divides P2.

Does P*Q*R always divide P+Q+R?
If not, give a counterexample.
If so, prove it.

No Solution Yet Submitted by K Sengupta    
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re: Analytical Solution | Comment 2 of 3 |
(In reply to Analytical Solution by Steve Herman)

Some values that work:
(1,1,1), (1,1,2), (1,2,3)

In the positive integers, this list looks exhaustive, the reason being that (1,1,x)  falls between 1 and 2, while (x,y,z), not necessarily distinct, is a fraction less than 1.

  Posted by broll on 2015-05-13 05:38:28
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