Consider the polynomial ring F [ x ] over a field F. Let d and...
Consider the polynomial ring over a field F. Let d and n be two nonnegative integers.
Answer & Explanation
Suppose . By division algorithm, we can write for some with . Now, observe that
Expanding the above, and cancelling many terms, we get that
Together with , this implies:
which gives . This is a contradiction, unless , in which case
The converse easily follows from the identity