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bute the order of 10 modulo 13. Compute the period of th /13.

bute the order of 10 modulo 13. Compute the period of th /13.

Advanced Engineering Mathematics
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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**Computation Task: Modular Arithmetic and Fraction Periodicity** 1. **Objective:** Compute the order of 10 modulo 13. 2. **Objective:** Compute the period of the fraction 1/13. ### Explanation: **1. Order of 10 modulo 13:** - The order of a number \( a \) modulo \( n \) is the smallest positive integer \( k \) such that \( a^k \equiv 1 \pmod{n} \). Here, you need to find the smallest \( k \) for which \( 10^k \equiv 1 \pmod{13} \). **2. Period of the fraction 1/13:** - To find the period, perform long division to express \( 1/13 \) as a decimal. The period is the length of the repeating sequence in the decimal expansion of this fraction.
Transcribed Image Text:**Computation Task: Modular Arithmetic and Fraction Periodicity** 1. **Objective:** Compute the order of 10 modulo 13. 2. **Objective:** Compute the period of the fraction 1/13. ### Explanation: **1. Order of 10 modulo 13:** - The order of a number \( a \) modulo \( n \) is the smallest positive integer \( k \) such that \( a^k \equiv 1 \pmod{n} \). Here, you need to find the smallest \( k \) for which \( 10^k \equiv 1 \pmod{13} \). **2. Period of the fraction 1/13:** - To find the period, perform long division to express \( 1/13 \) as a decimal. The period is the length of the repeating sequence in the decimal expansion of this fraction.
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