why is math so painful

[Destrus]

i used to like it, then i got to college

[Hessah]

-pat pat-

[Destrus]

i hate howwhile studying i look at the first exam and see that hey, i can do a lot ofthis pretty easily and i feel like i've actually gotten something done cause i looked it over so quickly but in reality i've barely scratched the surface of my problems

[Destrus]

how do i prove that for any natural number n n^4 - n^2 is divisible by 3

[Vasu]

Use mathematical induction!

[lamchopz]

n^4 - n^2 = n^2(n^2 - 1) = n*n*(n-1)*(n+1)

Since, n -1 ,n , n + 1 are three consecutive natural numbers, one of them has to be divisible by 3, hence your expression is divisible by 3.

[Vasu]

LOL, the method I was thinking of was, prove it for n=1, then assume it is true for n=k, and then prove it for n=k+1. A bit more elaborate.

[Destrus]

so that was a test question from the first exam i couldn't remember how to do (even then T_T). if he actually put it on the final i'd be so happy i might have to kiss you lam (but settle for a hug)


also, vasu, die a horrible death D:<
cause that's on this too and i hate it. i hate it soooo much.