Prove that for all integers n ≥ 1, 10" = (-1)" (mod 11). Use part (a) to prove that a positive integer is divisi- ble by 11 if, and only if, the alternating sum of its dig- its is divisible by 11. (For instance, the alternating sum of the digits of 82,379 is 8-2+3-7+9 = 11 and 82,379 11-7489.) =
Prove that for all integers n ≥ 1, 10" = (-1)" (mod 11). Use part (a) to prove that a positive integer is divisi- ble by 11 if, and only if, the alternating sum of its dig- its is divisible by 11. (For instance, the alternating sum of the digits of 82,379 is 8-2+3-7+9 = 11 and 82,379 11-7489.) =
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
Related questions
Question
![b.
13. a. Prove that for all integers n ≥ 1, 10" = (-1)" (mod 11).
Use part (a) to prove that a positive integer is divisi-
ble by 11 if, and only if, the alternating sum of its dig-
its is divisible by 11. (For instance, the alternating sum
of the digits of 82,379 is 8-2+3-7+9 = 11 and
82,379 11.7489.)
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e6203f-f751-4558-ba33-f371cf952d2b%2F07b0f553-0d4f-40ec-bafe-fe2d518617ea%2Fb9ddf7l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b.
13. a. Prove that for all integers n ≥ 1, 10" = (-1)" (mod 11).
Use part (a) to prove that a positive integer is divisi-
ble by 11 if, and only if, the alternating sum of its dig-
its is divisible by 11. (For instance, the alternating sum
of the digits of 82,379 is 8-2+3-7+9 = 11 and
82,379 11.7489.)
=
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