Select the mistake that is made in the proof given below. Theorem. The square of any odd integer is equal to a multiple of 4 plus 1. Proof. Since x is odd, x = 2k + 1 for some integer k. Plugging in the expression 2k + 1 for x gives x2 = (2k+1)2 = 4k2 + 4k + 1 = 4(k2 + k) + 1 Since k is an integer, k2 + k is also an integer. Therefore, 4(k2 + k) is a multiple of 4 and x2 equal to a multiple of 4 plus 1.
Select the mistake that is made in the proof given below. Theorem. The square of any odd integer is equal to a multiple of 4 plus 1. Proof. Since x is odd, x = 2k + 1 for some integer k. Plugging in the expression 2k + 1 for x gives x2 = (2k+1)2 = 4k2 + 4k + 1 = 4(k2 + k) + 1 Since k is an integer, k2 + k is also an integer. Therefore, 4(k2 + k) is a multiple of 4 and x2 equal to a multiple of 4 plus 1.
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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Select the mistake that is made in the proof given below.
Theorem. The square of any odd integer is equal to a multiple of 4 plus 1.
Proof.
Since x is odd, x = 2k + 1 for some integer k. Plugging in the expression 2k + 1 for x gives x2 = (2k+1)2 = 4k2 + 4k + 1 = 4(k2 + k) + 1
Since k is an integer, k2 + k is also an integer.
Therefore, 4(k2 + k) is a multiple of 4 and x2 equal to a multiple of 4 plus 1.
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