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Did you mean to put 2x+1? | Did you mean to put 2x+1? | ||
-Sarah | -Sarah | ||
| + | ------------------------------ | ||
| + | Yea, he or she did mean that. Look at the line: | ||
| + | |||
| + | <math>4x^2+2x+2x+1=1</math> from that you can see he or she multiplied <math>(2x+1)(2x+1)=1</math> | ||
| + | |||
| + | or it would look like <math>4x^2-2x-2x+1=1</math> | ||
Revision as of 16:35, 5 November 2008
Suppose the inverse of $ 2x-1 $ is $ 2x-1 $, then
$ (2x-1)(2x-1)=1 $
$ 4x^2+2x+2x+1=1 $
$ 4x^2+4x+1=1 $, but in $ Z_4[x] $, 4=0. so,
$ 0x^2+0x+1=1 $
$ 1=1 $
Therefore, $ 2x-1 $ has an inverse in $ Z_4[x] $ and specifically, that inverse is $ 2x-1 $
Did you mean to put 2x+1? -Sarah
Yea, he or she did mean that. Look at the line:
$ 4x^2+2x+2x+1=1 $ from that you can see he or she multiplied $ (2x+1)(2x+1)=1 $
or it would look like $ 4x^2-2x-2x+1=1 $
