13

Part of 2000 Harvard-MIT Mathematics Tournament

Problems(2)

2000 Guts #13: Polynomial division

Source:

Determine the remainder when

(x^4-1)(x^2-1)

1+x+x^2

algebrapolynomialgeometry3D geometry

2000 HMMT RMT Team #13 max no of intersections inside convex n-gon

Source:

P_1, P_2,..., P_n

n

-gon. If all lines

P_iP_j

are joined, what is the maximum possible number of intersections in terms of

n

obtained from strictly inside the polygon?

combinatoricscombinatorial geometrygeometry