Here is half of #2 . . .
We observe the following . . .
We have: .
. . Hence: .
Therefore, is three more than a mutiple of 4 . . . It cannot be a square.
I have a couple of questions 1 of which I more or less know what should be the proof, I just dont really know how to prove it.
1. My first question is how would I go about proving that m^2 = n^2
if and only if m = n or m = -n.
I know I have to prove it both ways, but am not quite sure how to construct it.
2. My next problem is proving that either 2x10^500 + 15 or 2x10^500 + 16
is not a perfect square.
Now I am fairly certain that perfect squares do not appear sequentially, thus proving that one of them is not square, but I am not sure how to exactly go about it.
The first question should probably be a proof that is fairly simple, these questions are both coming from chapters 1.6 and 1.7 of my book, so they shouldnt be too difficult.
help appreciated. Extra points to those who can help me understand a little bit more.
thank you guys for your help, what I am wondering although, is how in the HECK can you come up with some of these things?
Because I just started this class, should It be this kind of awkward for me to do, or come up with some of these proofs?
or rather, will it get easier as I practice?
Because I must tell you, some of these things that are coming up in these proofs are kind of ridiculoid, and while they make PERFECT sense, I am just not quite sure how I could come up with them myself.
And to tell you the truth, I am by no means bad at math in anyway, but this type of thinking really makes my head hurt.
Of course, I only started learning this, so one would assume I wont be very good at this, Im pretty sure its safe to also assume that not many people were very good at the start of this type of mathematics as well.
of course, I have been wrong before.