Hi.

I need to prove that n^4 - 4n^2 is divisible by 3.

The induction hypnosis would be k^4 - 4k^2 is indeed divisible by 3, for k >= 0.

What I don't understand is after we expand out (k+1) -4(k+1)^2, why do we need to subtract (n^4-4n)?

I know that n^4 - 4n = 3t for some integer t (divisible by 3).

http://courses.cs.vt.edu/~cs4104/heath/Spring2005/resources/induction.pdf

The answer is given somewhere in the middle.

Thanks!Hence (n+1)^4 - 4(n+1)2 is divisible by 3 if (n+1)^4 - 4(n+1)^2-(n^4 -4n^2)

is divisible by 3.