Solve the congruence.

8x ≡ 1 mod (27)

Thanks!

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- Mar 14th 2007, 11:00 AMMathStudent1Congruence Problem
Solve the congruence.

8x ≡ 1 mod (27)

Thanks! - Mar 14th 2007, 11:11 AMThePerfectHacker
gcd(8,27)=1 thus there exists a unique congruence class of solutions.

8x = 1 = -26 mod(27)

Thus,

8x = -26 (mod 27)

They share a factor of 2 which is coprime with 27, divide by it.

4x = -13 = 14(mod 27)

Again divide by it,

2x = 7 (mod 27)

Again,

2x = - 20 (mod 27)

x = -10 (mod 27)

Thus,

x = 17 (mod 27) - Mar 14th 2007, 11:25 AMMathStudent1
Thanks TPH. I am looking through it to see if it all makes sense.