perplexus.info :: Just Math : Relationship Satisfaction Settlement

Relationship Satisfaction Settlement (Posted on 2015-05-01)

Each of x and y is a positive integer such that x²+y divides (x-1)x(x+1).

Is the relationship y ≥ x true for every possible pair of x and y?

If so, prove it.
If not, provide a counterexample.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

Comment 1 of 1

We're given (x^2+y)*k = (x-1)x(x+1) for some positive integer k.

Assume x>y.

Then (x^2+x)*k > (x-1)x(x+1) and k > (x-1).

So (x^2+y)*k < k(x)(x+1) and y < x, contradicting the original assumption, and y >= x is true.

Posted by xdog on 2015-05-03 19:14:28

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