On a Zaremba’s Conjecture for Powers
DOI:
https://doi.org/10.5644/SJM.01.1.02Abstract
A conjecture of Zaremba says that for every $m\ge 2$ 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 ${c\cdot 2^n}$-th power of $7$ where $n\ge 0$ and $c=1,3,5,7,9,11$. A more general case is considered.
2000 Mathematics Subject Classification. 11A55
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References
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