perplexus.info :: Just Math : Product Divides Sum?

Product Divides Sum? (Posted on 2015-05-12)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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 2015-05-12 14:00:41

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