(27) SHOW YOUR WORK Find all four solutions to x^2 ≡ 4 176,381. Your values for x must be betwee

Name: (27) SHOW YOUR WORK Find all four solutions to x^2 ≡ 4 176,381. Your values for x must be between 0 176,380. You may use 176,381=233 * 757.
Uploaded: 2021-08-31T00:12:03-08:00
Duration: 43 s
Channel: Charles Machakwa
Description: (27) SHOW YOUR WORK Find all four solutions to x^2 ≡ 4 176,381. Your values for x must be between 0 176,380. You may use 176,381=233 * 757.

Step 1: Rewrite the equation x^(2) ≡ 4 (mod 176,381) as x^(2) ≡ 4 (mod 233) and x^(2) ≡ 4 (mod 7

Question

(27) SHOW YOUR WORK Find all four solutions to $x^2 \equiv 4 \pmod{176,381}$. Your values for $x$ must be between 0 & 176,380. You may use 176,381=233 * 757.

          (27) SHOW YOUR WORK Find all four solutions to $x^2 \equiv 4 \pmod{176,381}$. Your values for $x$ must be between 0 & 176,380. You may use 176,381=233 * 757.

(27) SHOW YOUR WORK Find all four solutions to x^2 ≡ 4 176,381. Your values for x must be between 0 176,380. You may use 176,381=233 * 757.

Added by Dolores S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Charles Machakwa

08/31/2021

Step 1

Step 2: Solve x^(2) ≡ 4 (mod 233) for x. To find the solutions for x mod 233, we can use the fact that 233 is a prime number. Since 233 is prime and 4 is a quadratic residue modulo 233, there are exactly two solutions for x mod 233. The solutions are x ≡ ±2 Show more…

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(27) SHOW YOUR WORK Find all four solutions to x^(2)-=4(mod176,381). Your values for x must be between 0&176,380. You may use 176,381=233**757. (27) SHOW YOUR WORK Your values for X 176,381=233*757. Find all four solutions to x'=4 (mod 176,381). must be between 0 176,380. You may use