(New page: It seems to me that |U(r)| x |U(s)| x gcd(r,s) = |U(rs)|. All of the integers in Problem 38 had a gcd of 1, but 4 and 10 have a gcd of 2. I thought of a couple other examples that this w...) |
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| + | =[[HW3_MA453Fall2008walther|HW3]], Chapter 3, Problem 40, [[MA453]], Fall 2008, [[user:walther|Prof. Walther]]= | ||
| + | ==Problem Statement== | ||
| + | ''Could somebody please state the problem?'' | ||
| + | |||
| + | ---- | ||
| + | ==Discussion== | ||
It seems to me that |U(r)| x |U(s)| x gcd(r,s) = |U(rs)|. All of the integers in Problem 38 had a gcd of 1, but 4 and 10 have a gcd of 2. I thought of a couple other examples that this works for (2 and 4 is a simple example that holds). | It seems to me that |U(r)| x |U(s)| x gcd(r,s) = |U(rs)|. All of the integers in Problem 38 had a gcd of 1, but 4 and 10 have a gcd of 2. I thought of a couple other examples that this works for (2 and 4 is a simple example that holds). | ||
-DK | -DK | ||
| + | --------------- | ||
| + | I thought that if Let U(r)=a U(s)=b if either one or both r or s is prime then |U(rs)|=2*(ab). Same thing you have but said differently | ||
| + | Jenny | ||
| + | ---- | ||
| + | [[HW3_MA453Fall2008walther|Back to HW3]] | ||
| + | |||
| + | [[Main_Page_MA453Fall2008walther|Back to MA453 Fall 2008 Prof. Walther]] | ||
Latest revision as of 17:06, 22 October 2010
HW3, Chapter 3, Problem 40, MA453, Fall 2008, Prof. Walther
Problem Statement
Could somebody please state the problem?
Discussion
It seems to me that |U(r)| x |U(s)| x gcd(r,s) = |U(rs)|. All of the integers in Problem 38 had a gcd of 1, but 4 and 10 have a gcd of 2. I thought of a couple other examples that this works for (2 and 4 is a simple example that holds).
-DK
I thought that if Let U(r)=a U(s)=b if either one or both r or s is prime then |U(rs)|=2*(ab). Same thing you have but said differently Jenny
