Can logarithms be applied to Modular arithmetic

[l-1j-cho]

I was just curious. I believe the answer would be no, but I don;t know why

 

[The Chaz]

I was just curious. I believe the answer would be no, but I don;t know why

I'm not sure of your background with modular arithmetic, so I'll just start small...
We consider all numbers with the same remainder after dividing by n to be EQUIVALENT.
For example, 2 = 5 = 8 = 11 = 300000000000002 = -1 mod 3. (Here, the "triple" bar sign would be better than the double bar equality, but I'm avoiding markup)

So in the case of n = 3, there are 3 classes: [0], [1], and [2].
We define addition by [x] + [y] = [x + y].
BUT, we have to check that this really is a function (i.e. that it is well-defined).

Similarly, we would have to check for such a definition including logarithms, but I think you'll find that we can't get anything consistent to work.

0 = ln[1] = ln[4] = 2ln[2] = 2*.6931... ?

 

[BenVitale]

This article may help you

http://www.cs.brown.edu/courses/cs007/oneway/node2.html

Cheers!

 

[l-1j-cho]

If that assumption were true...

Fermat’s Little Theorem states that
n^p ≡ n (mod p)
where n is an integer and p is a prime number
This implies
log (base n) n^p ≡ log (base n) n (mod p)
Therefore
p ≡ 1 (mod p)
In conclusion
0 ≡ 1 (mod p)

ha...

 

[I like Serena]

I was just curious. I believe the answer would be no, but I don;t know why

There's a thing called the discrete logarithm, that's been defined for modular arithmetic.
Calculating it is non-trivial.

From wikipedia: http://en.wikipedia.org/wiki/Discrete_logarithm

"a solution x of the equation g^x = h is called a discrete logarithm to the base g of h"