Question

For each integer 2 ? a ? 10, find the last four digits of a^1000. [Hint: We need to calculate a^1000 mod 10000. Use Euler's theorem and Chinese remainder theorem. For example, 10000 = 2^4 ? 5^4; 2^1000 ? 0 mod 2^4, and 2^500 ? 1 mod 5^4.]

Name: For each integer 2 ? a ? 10, find the last four digits of a^1000. [Hint: We need to calculate a^1000 mod 10000. Use Euler's theorem and Chinese remainder theorem. For example, 10000 = 2^4 ? 5^4; 2^1000 ? 0 mod 2^4, and 2^500 ? 1 mod 5^4.]
Uploaded: 2022-10-27T07:52:09-08:00
Duration: 3 min 29 s
Channel: Adi S
Description: For each integer 2 ? a ? 10, find the last four digits of a^1000. [Hint: We need to calculate a^1000 mod 10000. Use Euler's theorem and Chinese remainder theorem. For example, 10000 = 2^4 ? 5^4; 2^1000 ? 0 mod 2^4, and 2^500 ? 1 mod 5^4.]

          For each integer 2 ? a ? 10, find the last four digits of a^1000. [Hint: We need to calculate a^1000 mod 10000. Use Euler's theorem and Chinese remainder theorem. For example, 10000 = 2^4 ? 5^4; 2^1000 ? 0 mod 2^4, and 2^500 ? 1 mod 5^4.]

For each integer 2 ? a ? 10, find the last four digits of a^1000. [Hint: We need to calculate a^1000 mod 10000. Use Euler's theorem and Chinese remainder theorem. For example, 10000 = 2^4 ? 5^4; 2^1000 ? 0 mod 2^4, and 2^500 ? 1 mod 5^4.]

Added by Jose Manuel T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

10/27/2022

Step 1

Step 1: Calculate 3^1000 mod 16 using Euler's theorem. Show more…

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For each integer 2 ≤ a ≤ 10, find the last four digits of a^1000. [Hint: We need to calculate a^1000 mod 10000. Use Euler's theorem and Chinese remainder theorem. For example, 10000 = 2^4 ∙ 5^4; 2^1000 ≡ 0 mod 2^4, and 2^500 ≡ 1 mod 5^4.]