Open Research Index

Bounds for the iteration x ↦ a mod x

Jason Davies

Palomar Registrypalomar/PALOMAR-2026-10-27-000017Oct 27, 2026math.NTscore 0

For integers 0 0, including the external coefficient-uniform affine-curve theorem and the effective Hilbert specialisation sieve, and its rational instance 4317/14677. It also proves the exterior-lattice exponents 471/1559 - 6 sqrt(105)/7795 and 153/520, the joint-invariant exponents (1310-sqrt(655))/4365, 2201/7480 and 128/435 and the earlier exponents 45/152, 8/27, 11/37, 23/77, and 3/10. It also proves a bound O(a^(1/4) sqrt R), where R minus one counts rises in the quotient increments, and positivity and integrality of the orbit's Hankel invariants. A separate conditional theorem gives…

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