Sums of nearest integer continued fractions with bounded digits: ${\text{NICF}}_5+{\text{NICF}}_5=\mathbb{R}$

Wieb Bosma, Alex Brouwers

Adapting Cantor set methods that were used by Hall and Hlawka for regular continued fractions, we prove that every real number can be obtained as the sum of two real numbers for wh…