Rewrite all requests to index.php with nginx

Question

In my apache configuration I have the following simple rewrite rule which

1. unless file exists will rewrite to index.php
2. on the urls you never see the f

Answer 1

Here is what worked for me to solve part 1 of this question:

    location / {
            rewrite ^([^.]*[^/])$ $1/ permanent;
            try_files $uri $uri/ /index.php =404;
            include fastcgi_params;
            fastcgi_pass php5-fpm-sock;
            fastcgi_index index.php;
            fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
            fastcgi_intercept_errors on;
    }

rewrite ^([^.]*[^/])$ $1/ permanent; rewrites non-file addresses (addresses without file extensions) to have a "/" at the end. I did this because I was running into "Access denied." message when I tried to access the folder without it.

try_files $uri $uri/ /index.php =404; is borrowed from SanjuD's answer, but with an extra 404 reroute if the location still isn't found.

fastcgi_index index.php; was the final piece of the puzzle that I was missing. The folder didn't reroute to the index.php without this line.