Please help me to figure out how to produce with that:
I have the following code:
$$ gcd(0,0) = 0 $$
$$ gcd(u,v) = gcd(v,u) $$
$$ gcd(u,v) = gcd(-u,v) $$
$$ gcd(u,0) = |u| $$
$$
2^{x^3} = x+1/x\ge 2 = \pi\approx 3{,}14
$$
$$
x^{4357}+y^{4357}=z^{4357}
$$
This is what I need:

I don't want to align anything, I just want to remove the space between equations because I think it takes too much space. Anyway I don't like the view of my equations, looks like something is not good there (only with gcd, the other equations looks OK). One thing to fix that is probably to use "\gcd" instead of "gcd"... I'd like to have some advice how to make it look better and to resolve the original question with spacing between equations as well. I also looking for the most simple solution, without using complex ams-structures if possible.

\gcdshould be used; you want to look at thegather*environment ofamsmath. Never use$$in LaTeX (see Why is\[ … \]preferable to$$?). In Plain TeX there's\displaylinesfor centering multiple equations. – egreg Feb 14 '13 at 13:58