(New page: Chapter 13, Problem 5. Show that every nonzero element of Zn is a unit or a zero-divisor. Answer: Suppose that a is in Zn. If gcd(a, n) = 1, then we know that a is a unit. Suppose that ...) |
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| + | =[[HW7_MA453Fall2008walther|HW7]] (Chapter 13, Problem 5, [[MA453]], Fall 2008, [[user:walther|Prof. Walther]]= | ||
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| + | ==Question== | ||
| + | Show that every nonzero element of Zn is a unit or a zero-divisor. | ||
| + | ---- | ||
| + | ==Answer 1== | ||
| + | Suppose that a is in Zn. | ||
If gcd(a, n) = 1, then we know that a is a unit. | If gcd(a, n) = 1, then we know that a is a unit. | ||
Suppose that gcd(a, n) = d > 1. | Suppose that gcd(a, n) = d > 1. | ||
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-Neely Misner | -Neely Misner | ||
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| + | ==Answer 2== | ||
| + | Write it here. | ||
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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 08:50, 21 March 2013
Contents
HW7 (Chapter 13, Problem 5, MA453, Fall 2008, Prof. Walther
Question
Show that every nonzero element of Zn is a unit or a zero-divisor.
Answer 1
Suppose that a is in Zn. If gcd(a, n) = 1, then we know that a is a unit. Suppose that gcd(a, n) = d > 1. Then a(n/d)= (a/d)n = 0, so a is a zero-divisor.
-Neely Misner
Answer 2
Write it here.
