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## About Prove each of the following statements using mathematical induction. (a) Prove that for any positive integer n, 4 evenly divides 32n-1

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About Prove each of the following statements using mathematical induction. (a) Prove that for any positive integer n, 4 evenly divides 32n-1. (b) Prove that for any positive integer n, 6 evenly divides 7n – 1. (c) Prove that for any positive integer n, 4 evenly divides 11n – 7n. (d) Prove that for any positive integer n, 7 evenly divides 9n – 2n.

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5 months
2021-08-29T20:51:17+00:00
2021-08-29T20:51:17+00:00 1 Answers
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## Answers ( )

Answer:(a)

(b)

(c)

(d)

Step-by-step explanation:Solving (a): For integer, 4dividesThe proof is as follows:For n = k, we have:

Multiply through by 4Next, prove the statement is true forExpress -1 as – 9 + 8Factorize:Recall that:

So, we have:FactorizeSince the above mathematical statement is true, then the given statement has been provedSolving (b): For integer, 6dividesThe proof is as follows:For n = k, we have:

Multiply through by 6Next, prove the statement is true forExpress -1 as – 7 + 6Factorize:Recall that:So, we have:FactorizeSince the above mathematical statement is true, then the given statement has been provedSolving (c): For integer, 4dividesThe proof is as follows:For n = k, we have:

Multiply through by 4Next, prove the statement is true forCollect Like TermsRecall that:So, we have:FactorizeSince the above mathematical statement is true, then the given statement has been provedSolving (d): For integer, 7dividesThe proof is as follows:For n = k, we have:

Multiply through by 7Next, prove the statement is true forCollect Like TermsRecall that:So, we have:FactorizeSince the above mathematical statement is true, then the given statement has been proved