On Pascal triangles modulo a prime power Original Research Article

In the first part of the paper we study arithmetical properties of Pascal triangles modulo a prime power; the main result is the generalization of Lucasʹ theorem. Then we investigate the structure 〈N; Bpx〉, where p is a prime, α is an integer greater than one, and View the MathML source; it is shown that addition is first-order definable in this structure, and that its elementary theory is decidable.