You might start by trying to prove some statements about parity. Like an odd number times an odd number is always odd. Even number times anything is always even. Those are pretty straight forward. If you feel you already feel comfortable with those. Then really you should just find a good...
Also, if you scroll through the Calculus and beyond section you might find some exercises to try to prove.
Or.. you might prove that there are no positive integers ##a,b,## and ##c## such that for ##n \geq 3##
$$a^n + b^n = c^n$$.
:-p
Yeah, I think the problem is you can't possibly test all values for n. But if you are asking about the expression I posted in the op, that doesn't always work and simply describes the form of a specific type of prime number.
Whether it was proven that one cannot exist I'm not entirely sure, but as fas as application, there is a foundation offering a substantial sum of money to find one, 1 million dollars I think? :)
That doesn't sound completely "not-fun" but alas I don't have an over abundance a time And while I did get a free Mathematica license from my school I haven't installed it yet because my computer is well.. sub-par. :) maybe this summer..
This news is a little dated, but I still found it interesting and wanted to see what everyone else thought about this years discovery of a new "largest" prime: ##2^{(57,885,161)}-1## its 17,425,170 digits long and would span all 7 harry potter books twice. Written out in plain text it would take...
Depending on how much you mind paying. Mathematica is top of the line but has a hefty price tag, and can be a bit cumbersome. If you want something that is free, a little more user friendly, but much less "elegant." Winplot is good.
On a side note, many college campuses have Mathematica in...