MathDB

Integral points

Source: VMEO IV - Junior Division

August 6, 2016

number theoryalgebraanalytic geometry

Problem Statement

On Cartesian plane, given a line defined by

y=x+\frac{1}{\sqrt{2}}

. a) Prove that every circle has center

I\in d

and radius is

\frac{1}{8}

has no integral point inside. b) Find the greatest

k>0

such that the distance of every integral points to

d

is greater or equal than

k