Suppose n E Z, n 2 2. Let P(n) be the statement that there are integers p and q such that n = q2P, where p 2 0 and q is odd. In words, every integer n 2 2 can be written as a product where one factor is odd and the other is a power of 2, even if that power is 2º. a. Verify that P(n) is true for n = 2,3,4, ... 12. b. For some of the numbers in P(n), it should have been easy to verify the claim. Which are easy? For the others, how are earlier cases used to help verify? Use strong mathematical induction to prove that P(n) is true for every integer n 2 2. C.

Suppose n E Z, n 2 2. Let P(n) be the statement that there are integers p and q such that n = q2P, where p 2 0 and q is odd. In words, every integer n 2 2 can be written as a product where one factor is odd and the other is a power of 2, even if that power is 2º. a. Verify that P(n) is true for n = 2,3,4, ... 12. b. For some of the numbers in P(n), it should have been easy to verify the claim. Which are easy? For the others, how are earlier cases used to help verify? Use strong mathematical induction to prove that P(n) is true for every integer n 2 2. C.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Using complete sentences and terms such as Suppose, consider, then, so, thus if necessary.

Suppose n E Z, n > 2. Let P(n) be the statement that there are integers p and q such that n =
q2P, where p > 0 and q is odd. In words, every integer n > 2 can be written as a product where
one factor is odd and the other is a power of 2, even if that power is 2º.
a. Verify that P(n) is true for n = 2,3,4, ... 12.
b. For some of the numbers in P(n), it should have been easy to verify the claim. Which are
easy? For the others, how are earlier cases used to help verify?
Use strong mathematical induction to prove that P(n) is true for every integer n > 2.
X10.
С.

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