Beta-expansions of rational numbers in quadratic Pisot bases
Tomáš Hejda, Wolfgang Steiner · Acta Arithmetica · 2018
We study rational numbers with purely periodic Rényi $\beta$-expansions. For bases $\beta$ satisfying $\beta^2=a\beta+b$ with $b$ dividing $a$, we give a necessary and sufficient condition for all rational numbers $p/q\in[0,1)$ with $\gcd(q,b)=1$ to