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Sum Root Concern (
Posted on 20150314
)
Does there exist an integer n such that:
√(n1) + √(n+1) is a rational number?
If so, provide an example.
If not, prove the nonexistance of such an integer.
No Solution Yet
Submitted by
K Sengupta
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(1 votes)
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Computer solution (spoiler)
Comment 1 of 1
Just kidding. No computer was harmed in the solving of this problem.
If sqrt(n1)+sqrt(n+1) is rational, then so is its square.
Squaring gives 2n+2*sqrt(n^21), and this is clearly rational only if n = 1.
So n = 1 is the only possibility, but this possibility does not work,
because sqrt(0) + sqrt(2) is irrational.
So there is no such n.
Happy PiDay!
Posted by
Steve Herman
on 20150314 10:12:41
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