MathDB

For every

n

in the set

\mathrm{N} = \{1,2,\dots \}

of positive integers, let

r_n

be the minimum value of

|c-d\sqrt{3}|

for all nonnegative integers

c

and

d

with

c+d=n

. Find, with proof, the smallest positive real number

g

with

r_n \leq g

for all

n \in \mathbb{N}

Problem Statement