Question 29
Prove that there exists a real constant $c$ such that for any pair $(x, y)$ of real numbers, there exist relatively prime integers $m$ and $n$ satisfying the relation
$$\sqrt{(x-m)^2 + (y-n)^2} \lt c \log(x^2 + y^2 + 2).$$
(This problem was suggested by Daniel Kane.)
$$\sqrt{(x-m)^2 + (y-n)^2} \lt c \log(x^2 + y^2 + 2).$$
(This problem was suggested by Daniel Kane.)