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I suggest that gluing it is a bad idea. The moment of your force when pushing and shoving after a tough night out finished off by a curry could break the glue and lead to a very messy situation!!
Seriously, you need about size 6 by 100MM screws. I'd imagine your upstairs toilets are wooden floors unless you're in an apartment block. Bear in mind that you'll get away without lifting the toilet if it is over wood as you can screw into wood without drilling, but the last few turns will take it out of you big time. Having said that, personally I would think you should lift the toilet and pre drill as its so much easier.
If its over concrete, to get plugs in you have to remove the toilet. Doing this will be far more work that the 2 screws! make sure you drill in exactly the right place!!
Additionally, i think plumbers screw in with a bit of plumbers thread stuff when securing to floors. Not sure if its to prevent water going in to where the screws are or what, but I have defo seen it done with the thready/hairy stuff.