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| + | =[[HW7_MA453Fall2008walther|HW7]] (Chapter 13, Problem 10) [[MA453]], Fall 2008, [[user:walther|Prof. Walther]]= | ||
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I used the examples on page 249 to "give a reasonable interpretation". Is that what they want? | I used the examples on page 249 to "give a reasonable interpretation". Is that what they want? | ||
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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. | 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. | ||
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| + | I understand what you're saying for 1/2. It makes sense. But how does that follow for numbers like sqrt(-3)? | ||
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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. | ||
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| + | Interesting. I did the same thing, but quit early with sqrt(-3) = 2. Didn't try 5. | ||
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| + | [[HW7_MA453Fall2008walther|Back to HW7]] | ||
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| + | [[Main_Page_MA453Fall2008walther|Back to MA453 Fall 2008]] | ||
Latest revision as of 08:53, 21 March 2013
HW7 (Chapter 13, Problem 10) MA453, Fall 2008, Prof. Walther
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.
