Let n be a positive integer:
1.Factorize n^5-n^3 (which I got to be n^2(n+1)(n-1)) and show that it's divisible by 24.
2. Prove that 2^2n is divisible by 3.
3. If n-1 is divisible by three, show that n^3-1 is divisible by nine.
I can explain using words more or less why, but I struggle to put them into mathematical language.
Thanks in advance for your help.