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)

Comments: ( Back to comment list | You must be logged in to post comments.)

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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