MathDB

a) Prove that

a>0

exists such that for each natural number

n

, there exists a convex

n

-gon

P

in plane with lattice points as vertices such that the area of

P

is less than

an^3

.
b) Prove that there exists

b>0

such that for each natural number

n

and each

n

-gon

P

in plane with lattice points as vertices, the area of

P

is not less than

bn^2

.
c) Prove that there exist

\alpha,c>0

such that for each natural number

n

and each

n

-gon

P

in plane with lattice points as vertices, the area of

P

is not less than

cn^{2+\alpha}

.
Proposed by Mostafa Eynollahzade

Problem Statement