3 papers
math.NT2026
A geometric proof of Lagrange's theorem for continued fractions
Anton Lukyanenko, Joseph Vandehey
For regular continued fractions (CFs), points with finite expansions are exactly the rationals and, by Lagrange's theorem, points with eventually-periodic expansions are exactly th…
math.NT2024
On the th smallest part of a partition into distinct parts
Rajat Gupta, Noah Lebowitz-Lockard, Joseph Vandehey
A classic theorem of Uchimura states that the difference between the sum of the smallest parts of the partitions of into an odd number of distinct parts and the corresponding s…
math.NT2024
On the number of partitions of a number into distinct divisors
Noah Lebowitz-Lockard, Joseph Vandehey
Let be the number of partitions of into distinct squarefree divisors of . In this note, we find a lower bound for , as well as a…