hello everyone, I dont know how to do this question

(i) For n belongs to IN+, show that n^2 + n + 1 is never a square in IN+

(ii) Find all r in Z (integers) such that r^2 + r +1 is a squre in Z(integers)

Can you give me hints please?

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- Oct 24th 2009, 10:10 AM #1

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- Oct 24th 2009, 01:39 PM #2

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Hi

i) Assume then Can you conclude?

ii) Thanks to i), we know the only such that is a square are among the non positive integers. So let be a non positive integer, and define

If then is a square.

Assume

Then since we have .

Therefore, when is a square iff Can you conclude?

- Oct 25th 2009, 01:51 AM #3

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