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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…
opencontinued-fractions reciprocity-obstructions
07
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…
openreciprocity-obstructions thin-orbits
06
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 $\Psi_1$ …
openlocal-global-principle reciprocity-obstructions thin-orbits
05

Large-denominator conjecture for continued fractions avoiding squares