Question 6 Let n, m, and p be integers such that p = n + m. Prove by contradiction that if p is odd, then n or m must be odd (i.e. they can't both be even) and n or m must be even (i.e. they can't both be odd).

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 25E: Let ,, and be integers. Prove or disprove that implies or .
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Question 6
Let n, m, and p be integers such that p = n + m. Prove by contradiction that if p is odd,
then n or m must be odd (i.e. they can't both be even) and n or m must be even (i.e.
they can't both be odd).
Transcribed Image Text:Question 6 Let n, m, and p be integers such that p = n + m. Prove by contradiction that if p is odd, then n or m must be odd (i.e. they can't both be even) and n or m must be even (i.e. they can't both be odd).
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