If it's infinite, is it countable or uncountable infinite?
I am a newbie to this topic... I don't know what modular arithmetic for polynomials means. Can someone please give me a link where I can learn?
If it's infinite, is it countable or uncountable infinite?
I am a newbie to this topic... I don't know what modular arithmetic for polynomials means. Can someone please give me a link where I can learn?
There are $8$ coefficients to be determined. The lead coefficient cannot be $0$. So the number is $(6)(7^7)$.
You only have 6 or 7 (why not always 7?) choices for the coefficients. Thus the number is finite, and you should be able to figure it out for yourself....
All such polynomials look like: $ a_1 x^0 + a_2 x^1 + \cdots + a_n x^{n-1} + a_{n+1} x^{n}$ where $a_i \in \{ \color{blue}{0}, 1, \ldots, n-1 \}$ for $1 \le i \le n$ and $a_{n+1} \in \{1, 2, \dots, n-1 \}.$
So there are $\underbrace{n \times n \times \cdots \times n}_{n\text{ times}} \times (n-1) = n^n \times (n-1)$ such polynomials.