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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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Solution Analytical Solution | Comment 1 of 3
Counterexample

P= Q = R = 2

2 divides 4, 
but P*Q*R = 8 does not divide P+Q+R = 6

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In fact, it is hard to find values where P*Q*R does divide P+Q+R.

Among other problems, P*Q*R is almost always > P+Q+R

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

  Posted by Steve Herman on 2015-05-12 14:00:41
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