3

Part of 2019 Auckland Mathematical Olympiad

Problems(2)

min pos. integer in form (2^a - 2^b)/(2^c - 2^d) is odd (2019 Auckland MO J3)

Source:

x

be the smallest positive integer that cannot be expressed in the form

\frac{2^a - 2^b}{2^c - 2^d}

a

b

c

d

are non-negative integers. Prove that

x

oddnumber theory

each 2 of n polygons have a common point (2019 Auckland MO S3)

Source:

There is a finite number of polygons in a plane and each two of them have a point in common. Prove that there exists a line which crosses every polygon.

geometryPolygons