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Well, we know that -3 mod 7 = 4. So we ask what elements in <math>Z_7</math> square to get 4. 2^2 = 4. 5^2 = 25 = 4. So sqrt(-3) corresponds to 2 and 5. | Well, we know that -3 mod 7 = 4. So we ask what elements in <math>Z_7</math> square to get 4. 2^2 = 4. 5^2 = 25 = 4. So sqrt(-3) corresponds to 2 and 5. | ||
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| + | Interesting. I did the same thing, but quit early with sqrt(-3) = 2. Didn't try 5. | ||
Revision as of 19:17, 25 October 2008
I used the examples on page 249 to "give a reasonable interpretation". Is that what they want?
I think what they want is something like this...
1/2 should be the multiplicative inverse of 2. In mod 7, the mult. inverse of 2 is 4 (4*2 = 2*4 = 8 mod 7 = 1). So 1/2 mod 7 could be interpreted as 4. Similar logic for the others.
I understand what you're saying for 1/2. It makes sense. But how does that follow for numbers like sqrt(-3)?
Well, we know that -3 mod 7 = 4. So we ask what elements in $ Z_7 $ square to get 4. 2^2 = 4. 5^2 = 25 = 4. So sqrt(-3) corresponds to 2 and 5.
Interesting. I did the same thing, but quit early with sqrt(-3) = 2. Didn't try 5.
