JHR's MA315 quizpage

MA315
Discrete and Combinatorial Algebra

An outline of answers to quiz #7, Monday February 15:
1: y,y+1,y+2

2: Multiply the linear primes to get the factorable polynomials;

    y    y+1      y+2
y   y^2  y^2+y   y^2+2y
y+1     y^2+2y+1  y^2+2
y+2              y^2+y+1

The primes are y²+1, y²+y+2,y²+2y+2.

3:

[2,1]         3*3= 9
[1,1,1] (4+3+2+1)=10
Factorable     19

There are 27-19=8 prime polynomials of degree 3.

4:

[3,1]             8*3=24
[2,2]         (3+2+1)= 6
[2,1,1]     3*(3+2+1)=18
[1,1,1,1] (5+4+3+2+1)=15
Factorable            63

There are 81-63=18 prime polynomials of degree 4.

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