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For <math>\sqrt{-3}</math> you use the same approach. First you observe -3 mod 7 = 4. Then you ask, what element(s) in Z_7 that have been squared give you 4? If you test all the elements in Z_7 you'll find 2^2 = 4 and 5^2 = 25 = 4 so both 2 and 5 are reasonable interpretations for <math>\sqrt{-3}</math>. Hope this helps.<br> | For <math>\sqrt{-3}</math> you use the same approach. First you observe -3 mod 7 = 4. Then you ask, what element(s) in Z_7 that have been squared give you 4? If you test all the elements in Z_7 you'll find 2^2 = 4 and 5^2 = 25 = 4 so both 2 and 5 are reasonable interpretations for <math>\sqrt{-3}</math>. Hope this helps.<br> | ||
--[[User:Jniederh|Jniederh]] 14:00, 11 March 2009 (UTC) | --[[User:Jniederh|Jniederh]] 14:00, 11 March 2009 (UTC) | ||
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| + | i'm still having a bit of problems. can someone explain with either the other ones or made up examples | ||
Revision as of 17:04, 11 March 2009
For this problem you can consider things such as 1/2 as the multiplicative inverse of 2. Then you have to ask, what element in Z7 is an inverse of 2? 2*4=8 and 8=1 in Z7 so a reasonable interpretation for 1/2 is 4. You can find reasonable interpretations for the other expressions in a similar fashion.
--Jniederh 03:05, 11 March 2009 (UTC)
I understand what we are doing here, but what are we supposed to do for something like $ \sqrt{-3} $? --Podarcze 11:34, 11 March 2009 (UTC)
For $ \sqrt{-3} $ you use the same approach. First you observe -3 mod 7 = 4. Then you ask, what element(s) in Z_7 that have been squared give you 4? If you test all the elements in Z_7 you'll find 2^2 = 4 and 5^2 = 25 = 4 so both 2 and 5 are reasonable interpretations for $ \sqrt{-3} $. Hope this helps.
--Jniederh 14:00, 11 March 2009 (UTC)
i'm still having a bit of problems. can someone explain with either the other ones or made up examples
