3 papers
math.NT2026
Weakening the Legendre Conjecture
Marc Chamberland, Armin Straub
The world of primes has many gaps between evidence and theorems. Here, we review Legendre's conjecture on primes between consecutive squares and recent progress on the weaker quest…
math.NT2025
An alternating sum of the floor function of square roots
Marc Chamberland, Karl Dilcher
We show that the alternating sum of the floor function of , with ranging from 1 to , has an easy evaluation for all odd integers . This is in contrast to…
math.NT2025
Sums of the floor function related to class numbers of imaginary quadratic fields
Marc Chamberland, Karl Dilcher
A curious identity of Bunyakovsky (1882), made more widely known by Pólya and Szeg{\H o} in their ``Problems and Theorems in Analysis", gives an evaluation of a sum of the floor f…