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Product Divides Sum? (
Posted on 20150512
)
Each of P, Q and R is a positive integer such that P divides Q
^{2}
, Q divides R
^{2}
and R divides P
^{2}
.
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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)
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
/*****************************/
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 20150512 14:00:41
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