1. ## Congruence

Dear Masters

Can I ask why 7^879 (mod300) = 43 (mod300)?

I thought Euler totient funcion (300) = 80 so 7^879 = 7^-1 * 7^880 .
Then, how can I 7^-1 (mod 300)..?

I could not get the answer

pLeas help me out

2. ## Re: Congruence

Can I also ask if 49x = 3 (mod 80) is 67 (mod 80) ?

3. ## Re: Congruence

You can find 7^79 (mod 300) by repeated squaring - find 7^2, 7^4, 7^8, etc., then multiply the appropriate ones together.

The answer to your second question is obvious - 49*67 = 3283 which is 3 (mod 80).

- Hollywood

4. ## Re: Congruence

Hi, but the answer for 7^-1 is 43 (mod 80), and also can I ask -93 (mod 80) is 67 (mod 80)?