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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
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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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.) =
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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