I have stuck... I tried to rewrite simple URL like www.mydomain.com to www.mydomain.com/login/page
I tried several rewrite options and got loop "rewrite or internal redirection cycle while processing"
or 301 error .
Does anybody can help me?
I'm absolutely sure that I am making stupid mistakes, but....

tried something like this

server {
listen 80;
server_name www.example.com;
rewrite ^/(.*) http://example.com/$1 permanent;
}

or

"I'm absolutely sure that I am making stupid mistakes, but...."
Yes you are.

server {
listen 80;
server_name www.example.com;
rewrite ^/(.*) http://example.com/$1 permanent;
}

$1 doesn't exist
Make your regex simply ^ and not ^/(.*)

make sure you have a server block setup for what you're redirecting to - or else you get a loop