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On generalized square-full numbers in an arithmetic progression

Angkana Sripayap, Pattira Ruengsinsub, Teerapat Srichan (2022)

Czechoslovak Mathematical Journal

Let a and b . Denote by R a , b the set of all integers n > 1 whose canonical prime representation n = p 1 α 1 p 2 α 2 p r α r has all exponents α i ( 1 i r ) ...

On geodesics of phyllotaxis

Roland Bacher (2014)

Confluentes Mathematici

Seeds of sunflowers are often modelled by n ϕ θ ( n ) = n e 2 i π n θ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance 2 π θ for θ the golden ratio. We associate to such a map ϕ θ a geodesic path γ θ : > 0 PSL 2 ( ) of the modular curve and use it for local descriptions of the image ϕ θ ( ) of the phyllotactic map ϕ θ .

On Grosswald's conjecture on primitive roots

Stephen D. Cohen, Tomás Oliveira e Silva, Tim Trudgian (2016)

Acta Arithmetica

Grosswald’s conjecture is that g(p), the least primitive root modulo p, satisfies g(p) ≤ √p - 2 for all p > 409. We make progress towards this conjecture by proving that g(p) ≤ √p -2 for all 409 < p < 2 . 5 × 10 15 and for all p > 3 . 38 × 10 71 .

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