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An improved upper bound on the Ruzsa number
Yuchen Ding, Yu-Chen Sun, Lilu Zhao
Let be the least positive integer such that there exists a set with for which the number of ordered solutions of wi…
An improved lower bound for odd integers not of the form
Yuchen Ding, Yu-Chen Sun, Lilu Zhao
Let be sufficiently large and \[ N(x)=\big|\bigl\{n\le x:n\ \text{is odd and }n\ne p+2^a+2^b \textrm{ with } p \text{ a prime and } a,b\in \mathbb{N}\bigr\}\big|. \] Motivated…
Problems 66 and 67 on sums of residue classes and primes of András Sárközy's collection of unsolved problems
Yuchen Ding, Christian Elsholtz, Yu-Chen Sun
In this note, we discuss two problems of Sárközy (2001). In particular, we prove an optimal result on sumsets of sparse subset of primes.
Solutions to some sign change problems on the functions involving sums of divisors
Yuchen Ding, Hao Pan, Yu--Chen Sun
In this note, we solve some sign change problems on the functions involving sums of divisors posed by Pongsriiam recently.
A note on additive complements of the squares
Yuchen Ding, Yu-Chen Sun, Li-Yuan Wang +1
Let be the set of squares and be an additive complement of so that $\mathcal…