2011/02/20 by Apoloniusz Tyszka, Tyszka, Apoloniusz
Computer Science · Mathematics · #03D20 #11D99 #11U99 #Algebraic Geometry and Number Theory #Benford’s Law and Fraud Detection #Commutative Algebra and Its Applications #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1102.4122
openalex publication_date 2011/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let En=xi=1, xi+xj=xk, xi ⋅ xj=xk: i,j,k ∈ 1,...,n. There is an algorithm that for every computable function f:N->N returns a positive integer m(f), for which a second algorithm accepts on the input f and any integer n>=m(f), and returns a system S ⊆ En such that S has infinitely many integer solutions and each integer tuple (x1,...,xn) that solves S satisfies x1=f(n). For each integer n>=12 we construct a system S ⊆ En such that S has infinitely many integer solutions and they all belong to Zn\[-2^2n-1,2^2n-1]n.