Assignment 16 (assigned 2/27, due 2/29)

Continuing with section 5.1, do 3b on page 230.

Do #16 on page 140 using Theorem 3.30 and Corollary 3.32.  (No credit for going back to the definition of congruence.)  Then do #10 on page 231, proving the same theorem by induction.  (For this proof do not use congruence, only the definition of "divides".)

The recursion formula for the number of regions left in the plane when n lines are removed (none of them being parallel and no three intersecting in the same point) is f(n+1)=f(n)+n+1. Also note that f(0)=1. Using this recursion formula and the method of induction, prove that f(n)=(n^2+n+2)/2.