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Relationship Satisfaction Settlement (
Posted on 20150501
)
Each of x and y is a positive integer such that x
^{2}
+y divides (x1)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.
No Solution Yet
Submitted by
K Sengupta
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solution
Comment 1 of 1
We're given (x^2+y)*k = (x1)x(x+1) for some positive integer k.
Assume x>y.
Then (x^2+x)*k > (x1)x(x+1) and k > (x1).
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 20150503 19:14:28
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