數學 M.I. 急問~~~~~~~~~~

1.(a) prove that (x^(n) -1)(x^(n+1) -1)is divisible by (x-1)(x^(2) -1)
(b)prove that (x^(n) -1)(x^(n+1) -1)(x^(n+2) -1) is divisible by (x-1)(x^(2) -1)(x^(3) -1)

2.(a) prove that a^(n+1)-(a^n)(b)>a(b^n)-b^(n+1)
(b)prove that a^(n+1)>b^n((n+1)a-nb)
(c)By using the result in(b),prove that (1+1/n)^n < (1+ 1/(n+1))^(n+1)
3.For any natural number n>7,prove that n=3p+5q for some non-negative integersp and q.


ThXX~~~~~~