Final answer:
To find the number of monic irreducible polynomials of degree 17 over ℤ11, we can use the formula (q^n - q) / n, where q is the number of elements in the field and n is the degree of the polynomial. Using q = 11 and n = 17, we find that there are approximately 9.885 x 10^14 monic irreducible polynomials over ℤ11.
Step-by-step explanation:
To find the number of monic irreducible polynomials of degree 17 that are over ℤ11, we can use the fact that the number of irreducible polynomials of degree n over a finite field with q elements is equal to the number of monic irreducible polynomials of degree n over the same field.
For polynomials of degree 17 over ℤ11, the number of irreducible polynomials will be the same as the number of monic irreducible polynomials, since every polynomial over ℤ11 can be scaled to be monic.
To find the number of monic irreducible polynomials, we can use the formula:
Number of monic irreducible polynomials of degree n over a field with q elements = (q^n - q) / n
Using q = 11 and n = 17, we can calculate the number of monic irreducible polynomials of degree 17 over ℤ11 as:
(11^17 - 11) / 17 ≈ 9.885 x 10^14