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- Show that (a + b)" = a + bn mod 2 for all integers a, b, and n with n > 0. Hint: Try looking at the cases where a is even (b can be either even or odd) or b is even (a can be either even or odd) and the case where both a and b are odd. 40

- Show that (a + b)" = a + bn mod 2 for all integers a, b, and n with n > 0. Hint: Try looking at the cases where a is even (b can be either even or odd) or b is even (a can be either even or odd) and the case where both a and b are odd. 40

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 57E
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5. Show that (a + b)n = a + bn mod 2 for all integers a, b, and n with n > 0. Hint: Try looking at the cases where a is even (b can be either even or odd) or b is even (a can be either even or odd) and the case where both a and b are odd.
Transcribed Image Text:5. Show that (a + b)n = a + bn mod 2 for all integers a, b, and n with n > 0. Hint: Try looking at the cases where a is even (b can be either even or odd) or b is even (a can be either even or odd) and the case where both a and b are odd.
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