3. Problem 7.5.2 part b. Note that we have already proved the case m = 2 since we know that [x]n[x] = [x -x]

Algebra & Trigonometry with Analytic Geometry
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ISBN:9781133382119
Author:Swokowski
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Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
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Problem 3 needed Read the instructions fron one pic and read the statement 2nd picture Please provide me hundred percent efficient solution in the order to get positive feedback
3.
7.5.2 (a) Prove the second half of Theorem 7.18, that is well-defined.
'n
(b) Prove by induction that the operation of raising to the pow. m E N is well-defined in Zn.
I.e., prove that
\m € N, \[x] € Z/~„ we have [x™] = [x]”.
n
Be careful! n is fixed, your induction variable is m. What base case(s) do you need?
Transcribed Image Text:3. 7.5.2 (a) Prove the second half of Theorem 7.18, that is well-defined. 'n (b) Prove by induction that the operation of raising to the pow. m E N is well-defined in Zn. I.e., prove that \m € N, \[x] € Z/~„ we have [x™] = [x]”. n Be careful! n is fixed, your induction variable is m. What base case(s) do you need?
3. Problem 7.5.2 part b. Note that we have already proved the case m = 2 since we know
that [x]n[x] = [x -x]
Transcribed Image Text:3. Problem 7.5.2 part b. Note that we have already proved the case m = 2 since we know that [x]n[x] = [x -x]
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