3 problems

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Large-denominator conjecture for continued fractions avoiding squares
Let $v$ be a non-square integer with $v\geq10^{13}$ . Consider rational numbers with continued fraction expansions … where the $a_i$ are positive integers. Large-denominator continu…
Conjectureopencontinued-fractions reciprocity-obstructionsarXiv posted 2 days ago
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Explicit numerator conjecture for the orbit of $\Psi_1$
Let … and consider its orbit of the indicated vector. Explicit $\Psi_1$ numerator conjecture. Every non-square integer $n>10569$ appears as a numerator in the orbit…
Conjectureopenreciprocity-obstructions thin-orbitsarXiv posted 2 days ago
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Local-global conjecture for the semigroup orbit of $\Psi_1$
Define … The table of congruence and reciprocity obstructions specifies the stated restrictions on numerators and denominators in these orbits. Local-global conjecture for $\Psi_1$ …
Conjectureopenlocal-global-principle reciprocity-obstructions thin-orbitsarXiv posted 2 days ago

Large-denominator conjecture for continued fractions avoiding squares