(1) Prove or disprove the following:
a: n^7-n is divisible by 7
b: n^9-n is divisible by 9
(2) Prove that a^3+b^3+c^3 is greater than or equal to 3abc
(3) Find 1000 consecutive composite integers.
(4) Show that 2^(2^n) +1 and 2^(2^m) +1 are relatively prime.