Show that for each n=1, 2, 3, . . ., we have n<2n.
Show that n2+n+1 is not divisible by 5 for any natural number n.
Given a natural number n, find a formula for the number of k less than n such that k is coprime to n. Prove that the formula works.
Prove for any natural number n that (n+1)(n+2)...(2n) is divisible by 2n.