Problem 4
For a real number x, let floor(x) be the greatest integer not exceeding x. Prove that floor((n-1)! divided by n(n+1)) is even for every positive integer n.
Step 5 of 5: Finish all cases
Detailed analysis
Every positive n is covered by the small cases, the two-composite case, or one of the two prime cases. In each case F_n is even, proving the assertion.