# 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.

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