The largest cycles consist by the quadratic residues and Fermat primes
Haifeng Xu
TL;DR
This paper investigates the maximum cycle lengths formed by quadratic residues modulo primes, providing formulas for these lengths, especially focusing on Fermat primes, to advance understanding of their structure.
Contribution
It introduces new formulas for the maximum cycle lengths of quadratic residues, including specific results for Fermat primes, enhancing theoretical knowledge in number theory.
Findings
Formulas for maximum cycle lengths of quadratic residues
Specific results for Fermat primes
Enhanced understanding of quadratic residue cycles
Abstract
This paper studies the largest cycles consisted by the quadratic residues modulo prime numbers. We give some formulae about the maximum length of the cycles. Especially, the formula for modulo Fermat primes is given.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · History and Theory of Mathematics