prime factorization of C(2N, N).
b) Find a good upper bound for C(2N, N).
c) Use a) and b) to show that ϑ(x) = O(x).
(2) Calculate lcm[1, 2,...,N] in terms of ψ(N).
time it is not, you lose one dollar. Should you accept these bets?
(8) Show that n! is never a square for n ≥ 2.