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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
Partial Lucas-type congruences
Armin Straub
In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes satisfies congruences that are a…
math.NT2024
Criteria for the integrality of th roots of power series
John Pomerat, Armin Straub
Heninger, Rains and Sloane raised the question of which power series with integer coefficients can be written as the th power of another power series with integer coefficients a…