2

Part of 1993 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1993 Problem 1.2

Source: Bundeswettbewerb Mathematik 1993 Round 1

M

be a finite subset of the plane such that for any two different points

A,B\in M

there is a point

C\in M

ABC

is equilateral. What is the maximal number of points in

M?

geometrycombinatoricscombinatorial geometryEquilateralPlane

only 1 square with vertices on graph of y = x^3 + ax

Source: 1993 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2

For the real number

a

it holds that there is exactly one square whose vertices are all on the graph with the equation

y = x^3 + ax

. Find the side length of this square.

analytic geometrysquaregeometry