13. a. Prove that for every integer n 1, 10" = (-1)" (mod 11). |
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
**13. a.** Prove that for every integer \( n \geq 1 \),
\[ 10^n \equiv (-1)^n \pmod{11} \]
**Explanation:**
The problem asks for a proof that for any integer \( n \) greater than or equal to 1, raising 10 to the power \( n \) and taking the modulo 11 of the result is equivalent to raising -1 to the power \( n \) and taking the modulo 11 of the result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3304c366-ad6f-4bcb-a67a-574f5df008af%2F4ff600cf-037e-4b78-ab25-3cecf2f46905%2F1owqn9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
**13. a.** Prove that for every integer \( n \geq 1 \),
\[ 10^n \equiv (-1)^n \pmod{11} \]
**Explanation:**
The problem asks for a proof that for any integer \( n \) greater than or equal to 1, raising 10 to the power \( n \) and taking the modulo 11 of the result is equivalent to raising -1 to the power \( n \) and taking the modulo 11 of the result.
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