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a. Prove that for every integer n 0, 10" = 1 (mod 9). b. Use part (a) to prove that a positive integer is divisible by 9 if, and only if, the sum of its digits is divisible by 9.

a. Prove that for every integer n 0, 10" = 1 (mod 9). b. Use part (a) to prove that a positive integer is divisible by 9 if, and only if, the sum of its digits is divisible by 9.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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**a.** Prove that for every integer \( n \geq 0 \), \( 10^n \equiv 1 \pmod{9} \). **b.** Use part (a) to prove that a positive integer is divisible by 9 if, and only if, the sum of its digits is divisible by 9.
Transcribed Image Text:**a.** Prove that for every integer \( n \geq 0 \), \( 10^n \equiv 1 \pmod{9} \). **b.** Use part (a) to prove that a positive integer is divisible by 9 if, and only if, the sum of its digits is divisible by 9.
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