On a Zaremba’s Conjecture for Powers - Komatsu, Takao (Sarajevo Journal of Mathematics, 2024)
A conjecture of Zaremba says that for every m2 there exists a reduced fraction a/m such that its simple continued fraction has all its partial quotients bounded by 5. This conjecture is proved with all partial quotients bounded by 3 for m being c· 2^n-th power of 7 where n0 and c=1,3,5,7,9,11. A more general case is considered. 2000 Mathematics Subject Classification. 11A55