Problems 66 and 67 on sums of residue classes and primes of András Sárközy's collection of unsolved problems

2025/08/04 by Ding, Yuchen, Elsholtz, Christian, Sun, Yu-Chen
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.02433

Abstract

In this note, we discuss two problems of Sárközy (2001). In particular, we prove an optimal result on sumsets of sparse subset of primes.

Citations

• Density ternary Goldbach for primes in a fixed residue class
• On the representation of large even integers as the sum of eight primes from positive density sets
• Density versions of the binary Goldbach problem
• The ternary Goldbach problem with primes in positive density sets
• An asymptotic formula for Goldbach's conjecture with monic polynomials in ℤ[θ][x]
• On sums of sparse prime subsets

Related

• Additive decompositions of sets with restricted prime factors
• Products in Residue Classes
• An explicit sum-product estimate in \mathbbF_p
• On products of primes and square-free integers in arithmetic\n progressions
• Slightly improved sum-product estimates in fields of prime order