[ ] True or False: There exist non-zero polynomials such that
Given that
By replacing with ,
we obtain :
then multiply it by
There are and on the both sides , delete them . The remaining is :
Repeat this procedure again ,
we obtain
then mutiply it by , the reference equation .
I find that comparing with the previous equation , eg
there is an extra linear factor on each side in and a change to and to , so I assume it is also true that :
Then at least one of them contains many factors , so it is not a polynomial .