Let F ={0 , 1 , a , b} be a field with four elements.

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The discussion centers on the field F = {0, 1, a, b}, which contains four elements. The calculations for a + b² and a² + b² yield results of b and 1, respectively. Participants express skepticism regarding the validity of the first equation, with one user requesting a multiplication and addition table for clarification. The consensus is that the answers provided are correct, despite initial doubts.

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Let F ={0 , 1 , a , b} be a field with four elements. What is a + b^2 and a^2 + b^2.

Apparently, the answers are b and 1, respectively. How do we come to that conclusion?
 
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rayne said:
Let F ={0 , 1 , a , b} be a field with four elements. What is a + b^2 and a^2 + b^2.

Apparently, the answers are b and 1, respectively. How do we come to that conclusion?

Hi rayne!

Can you set up a multiplication table?
And an addition table?
 
Btw, I do not believe that a + b^2 = b.
There seems to be a mistake in the problem statement.
 

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