How can I show these polynomials are not coprime? x,\ x-1

Malachi Novak 2022-04-24 Answered
How can I show these polynomials are not co'?
x, x1 and x+1 in the ring Z6[x]
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Answers (1)

veceritzpzg
Answered 2022-04-25 Author has 16 answers
Step 1
The ideal (x1, x+1) equals the ideal
(2, x1) and this is not the whole ring, otherwise
1(2, x1), so 1=2f(x)+(x1)g(x).
Now send x to 1 and get a contradiction.
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