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?
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.
Then since we have .
Therefore, when is a square iff Can you conclude?