I am working a combinatorial question. I need to decide when the following function m(7m^2 - 22m +7)/sqrt((m^2- 2m + 9)(9m^2 - 2m +1)) takes$$\frac{m(7m^2 - 22m +7)}{ \sqrt{ (m^2- 2m + 9)(9m^2 - 2m +1) } } $$takes integer values with following assumption:
- m takes all positive integer values
- (m^2- 2m + 9)(9m^2 - 2m +1) is a perfect square(= n^2 for some integer n).
1) m takes all positive integer values; 2) $(m^2- 2m + 9)(9m^2 - 2m +1)$ is a perfect square (= $n^2$ for some integer $n$). Limited computation for m < 20000$m < 20000$ shows m = 1, 5$m = 1, 5$.
Many thanks, Jianmin
