>With number theory, progress is much harder, things work in a completely different logic (think for example that 5+3 can be 0 for example)

I wasn't aware that the modulo operation had been raised to a field of mathematics.

Modulo operations is part of "number theory 101"

And ok, addition is nice and fun. Then you go to multiplication

Then you end up with Galois Fields.

Never underestimate the amount of discussion that goes into things like 1+1=2

> ...for example that 5+3 can be 0 for example

When is that example true? It seems like you made that up.

mod 8?

Hardly the 'mystery of number theory' the poster was talking about. There was no 'mod 8' syntax expressed in the example.

Yes, it is http://en.wikipedia.org/wiki/Modular_arithmetic

But you don't need to write "mod 8" in a congruence class

Oh, you want "the mystery of number theory" you can start with http://en.wikipedia.org/wiki/Fermat%27s_little_theorem

It was solved, and he (Fermat) was likely wrong, given the resulting proof.

(5 + 3) % 8 = 0 is not the same as 5 + 3 = 0

I'm not looking for mystery, I'm wondering why people think it exists, and are faking its existence by being imprecise.