16. Prove that an integer (a,-1an-2 · . . ao)10 is divisible by 11 if and only if ao + a2 + a4 + . . . = aj + a3 + a5 + · ·. (mod 11). [Hint: 10 = -1 (mod 11).] %3D

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 35E
icon
Related questions
Question
16. Prove that an integer (a,-jan–2 .. .ao)10 is divisible by 11
if and only if ao + a2 + a4 +..
(mod 11). [Hint: 10 = -1 (mod 11).]
= aj + a3 + a5 +·… ·
Transcribed Image Text:16. Prove that an integer (a,-jan–2 .. .ao)10 is divisible by 11 if and only if ao + a2 + a4 +.. (mod 11). [Hint: 10 = -1 (mod 11).] = aj + a3 + a5 +·… ·
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer