Y by
First, suppose that . Note that we can find a polynomial of that is not irreducible. We can consider, for example, . Fix and consider the polynomial . Suppose towards a contradiction that with . Note that we have at least one such that . Indeed, if for every , then the constant coefficient of is at least . However if , then we have that , which is a contradiction with the irreducibility of . This proves the result.
This post has been edited 1 time. Last edited by aeemc2, Sep 19, 2024, 2:06 PM
Reason: Add a correction that Dr. Gotti pointed out.
Reason: Add a correction that Dr. Gotti pointed out.