ITT: QTDDTOT

Lads I've been stuck on a question for quite some time now, and I'm hoping one of you can figure it out. It's my first time posting here and the question is simple to formulate, so I won't type it in latex (I'd just mess it up).
Here goes: Given a bounded hyperplane, how to determine if it contains any points where all of the coordinates are integer.
So basically, the plane is given by an equation a_1x_1 + a_2x_2 + ... + a_nx_n = g, and it is bounded by several equations b_1x_1 + .. + b_nx_n

shit nigger that actually sounds pretty hard

for A) and B) what you're looking for is called solving diophantine equations. You can probably find some material in your language on it.

C) looks tricky, try to read up about diophantine geometry to see if there's a general solution to that

Are the a_i integers, rational or arbitrary reals?

If the a_i are integers or rationals, then it's basically about modular arithmetic. If there's a single integer solution to the plane equation, there are infinitely many, forming an (n-1)-dimensional grid.

I'm trying to pay for a parking permit at my college and they are asking for plate type. It's just a regular car.

I believe i asked this in the past but I dont recall getting an answer.

Light can bend around the gravity well of a large star or black hole correct? Which is why we can see objects that are directly behind a large mass that really should be obfuscated from our view.

Does this not occur on both sides of the gravity well? Are many of the stars and galaxies in the sky duplicated?

All coefficients are arbitrary real numbers
Thanks! I'll look into that

Forgot pic

Maybe i dont understand but I feel like that just doesnt make sense. log8 and log5 are really just arbitrary decimals. The simplest form would be log5*a/a which I mean if you needlessly expanded out you could write as log13/a.

Nevermind, figured it out.