(b) Proposition. For each integer m, 5 divides (m-m). Proof. Let m e Z. We will prove that 5 divides (m³ - m) by proving that (m - m) =0 (mod 5). We will use cases. For the first case, if m = 0 (mod 5), then m = 0 (mod 5) and, hence, (m3 – m) = 0 (mod 5). For the second case, if m = 1 (mod 5), then m = 1 (mod 5) and, hence, (ms -m) = (1 – 1) (mod 5), which means that (m3 - m) = 0 (mod 5). For the third case, if m = 2 (mod 5), then m = 32 (mod 5) and, hence, (m- m) = (32-2) (mod 5), which means that (m- m) = 0(mod 5).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 46E
icon
Related questions
Topic Video
Question
I've been stuck on this one for a while. If the proposition is false, and the proof is incorrect, find the error in the proof and provide a counter example showing that it is false If the proposition is true, but the proof is wrong, fix the proof If everything is correct, nothing needs to be done
hence, (2a +b) = 0 (mod 3).
(b) Proposition. For each integer m, 5 divides (m - m).
Proof. Let m e Z. We will prove that 5 divides (m – m) by proving
that (m-m) = 0 (mod 5). We will use cases.
For the first case, if m = 0 (mod 5), then m5 = 0 (mod 5) and, hence,
(m – m) = 0 (mod 5).
For the second case, if m = 1 (mod 5), then m = 1 (mod 5) and,
hence, (m5- m) = (1– 1) (mod 5), which means that (ms- m) =
0 (mod 5).
For the third case, if m = 2 (mod 5), then m5
hence, (m3 - m) = (32- 2) (mod 5), which means that (m - m) =
0 (mod 5).
= 32 (mod 5) and,
BY NC SA
Transcribed Image Text:hence, (2a +b) = 0 (mod 3). (b) Proposition. For each integer m, 5 divides (m - m). Proof. Let m e Z. We will prove that 5 divides (m – m) by proving that (m-m) = 0 (mod 5). We will use cases. For the first case, if m = 0 (mod 5), then m5 = 0 (mod 5) and, hence, (m – m) = 0 (mod 5). For the second case, if m = 1 (mod 5), then m = 1 (mod 5) and, hence, (m5- m) = (1– 1) (mod 5), which means that (ms- m) = 0 (mod 5). For the third case, if m = 2 (mod 5), then m5 hence, (m3 - m) = (32- 2) (mod 5), which means that (m - m) = 0 (mod 5). = 32 (mod 5) and, BY NC SA
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell