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Here is a suggestion: The book says that the set of units of Zn is U(n). That is why I thought that they could write the gcd(k,n)=1 part. As far as the k(n/d)=0 part, they have in the back: | Here is a suggestion: The book says that the set of units of Zn is U(n). That is why I thought that they could write the gcd(k,n)=1 part. As far as the k(n/d)=0 part, they have in the back: | ||
| − | k(n/d)=sd(n/d)=sn=0. What I understood from that was that sn is equal to zero because Zn is a set under (addition/multiplication?) modulo n, so k is a zero divisor by definition of zero divisor. That is what I tried to piece together about it. | + | k(n/d)=sd(n/d)=sn=0. What I understood from that was that sn is equal to zero because Zn is a set under (addition/multiplication?) modulo n, so k is a zero divisor by definition of zero divisor. That is what I tried to piece together about it. -Josie |
Revision as of 18:13, 10 March 2009
Anyone have an idea on the explanation in the back of the book? I dont get where if gcd(k,n)=1 that means its a unit...and why does k(n/d)=0? I may just be not seeing something...any suggestions? -K. Brumbaugh
Here is a suggestion: The book says that the set of units of Zn is U(n). That is why I thought that they could write the gcd(k,n)=1 part. As far as the k(n/d)=0 part, they have in the back: k(n/d)=sd(n/d)=sn=0. What I understood from that was that sn is equal to zero because Zn is a set under (addition/multiplication?) modulo n, so k is a zero divisor by definition of zero divisor. That is what I tried to piece together about it. -Josie
