Prime Fields

[Guest]

Hello All,
Please I need Help in those Question
1) Determine the number of irreducible polynomials of degrees 2, 3, and 6 over the prime field Fp.
Hint: Count all polynomials of a given degree. Which of these are reducible?
2)Construct fields of order 22, 23 and 26

[GeradHum]

Use the formula counting irreducible polynomials over Fp:
Number = (1/n) * sum_{d|n} μ(d) * p^{n/d}
for degrees 2, 3, and 6, where μ is the Möbius function.

To construct fields of order p^n (like 2², 2³, 2⁶), take Fp and extend it by an irreducible polynomial of degree n over Fp.