[seqfan] Re: Integer ratio

[israel at math.ubc.ca]

If A = (n-1) (n^2 - n + 1) and B = 2n^2 - 2n + 1, note that
(n-1) and B are coprime (since B = 2 n (n-1) + 1)
and n^2 - n + 1 and B are coprime (since B = 2 (n^2 - n + 1) - 1).
So A and B are coprime, and A/B is never an integer unless B = +- 1
(which is when n = 0 or 1, making A/B = -1 or 0.

Cheers,
Robert Israel

On Mar 5 2021, Antreas Hatzipolakis wrote:

>In a geometric problem (*) appeared the ratio
>
>a/b = a(n) = (n - 1) (n^2 - n +1) / (2n^2 - 2n + 1)
>
>Questions
>1. For which n's (if any) a(n) is an integer?
>2. For which n's Sigma a(n) [sum of a(i), i = 1 to n] is integer?
>
> (*) 
> https://www.facebook.com/103907057666827/photos/a.103973994326800/503212241069638
>
>APH
>
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