- #1
Ed Aboud
- 201
- 0
Hi all.
Can someone please tell me what is going wrong here.
Solve
[tex] 12x \equiv 1(mod5) [/tex]
[tex]gcd(12,5) = 1 [/tex]
By Euclid's Algorithm =>
[tex] 1 = 5.5 - 2.12 [/tex]
So r is 5 in this case.
[tex] x = r ( \frac{b}{d} )[/tex]
Where b is 1 and d = gcd(12,5) = 1
[tex] x = 5 ( \frac{1}{1} ) [/tex]
[tex] x = 5 [/tex]
Ok fair enough but then I solve the congruence using
[tex] x \equiv b a^\phi^(^m^)^-^1 (mod m) [/tex]
[tex] x \equiv (1) 12^3 (mod5) [/tex]
[tex] x \equiv 3 (mod 5 ) [/tex]
I know this is the correct solution but what did I do wrong in the other one.
Thanks for the help!
Can someone please tell me what is going wrong here.
Solve
[tex] 12x \equiv 1(mod5) [/tex]
[tex]gcd(12,5) = 1 [/tex]
By Euclid's Algorithm =>
[tex] 1 = 5.5 - 2.12 [/tex]
So r is 5 in this case.
[tex] x = r ( \frac{b}{d} )[/tex]
Where b is 1 and d = gcd(12,5) = 1
[tex] x = 5 ( \frac{1}{1} ) [/tex]
[tex] x = 5 [/tex]
Ok fair enough but then I solve the congruence using
[tex] x \equiv b a^\phi^(^m^)^-^1 (mod m) [/tex]
[tex] x \equiv (1) 12^3 (mod5) [/tex]
[tex] x \equiv 3 (mod 5 ) [/tex]
I know this is the correct solution but what did I do wrong in the other one.
Thanks for the help!