11

Part of 1998 Moldova Team Selection Test

Problems(1)

max AP/PE in lattice ZxZ, unique P lies interior to ABC

Source: Stars O f Mathematics 2009 p3 - 1998 Moldova TST p11

A,B,C

be nodes of the lattice

Z\times Z

such that inside the triangle

ABC

lies a unique node

P

of the lattice. Denote

E = AP \cap BC

. Determine max

\frac{AP}{PE}

, over all such configurations.

lattice pointslatticemaximumratiogeometry