Hi all.(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Linear congruence

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