13 papers · 1 filter
Additive decompositions of multiplicative subgroups in prime fields: a self-contained approach
Chi Hoi Yip, Semin Yoo
Sárközy conjectured that the nonzero quadratic residues modulo a sufficiently large prime have no nontrivial additive decomposition. Hanson and Petridis proved the conjecture for…
Multiplicative subgroups are not restricted sumsets
Chi Hoi Yip, Semin Yoo
We determine exactly which proper multiplicative subgroups of a prime field can be represented as a restricted sumset of the form $A\mathbin{\widehat{+}} A=\{a+a':a,a'\in A,\ a\ne…
Extensions of the Carlitz-McConnel and Blokhuis-Sziklai theorems for unions of cyclotomic classes
Maosheng Xiong, Chi Hoi Yip
Let be a prime, let , and let . A celebrated result of Carlitz and McConnel states that if is a proper subgroup of ,…
Multiplicative irreducibility of small perturbations of the set of shifted -th powers
Chi Hoi Yip
Motivated by a conjecture of ErdÅs on the additive irreducibility of small perturbations of the set of squares, recently Hajdu and Sárközy studied a multiplicative analogue of t…
Multiplicatively reducible subsets of shifted perfect -th powers and bipartite Diophantine tuples
Chi Hoi Yip
Recently, Hajdu and Sárközy studied the multiplicative decompositions of polynomial sequences. In particular, they showed that when , each infinite subset of $\{x^k+1:…
Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
In this paper, we investigate the multiplicative structure of a shifted multiplicative subgroup and its connections with additive combinatorics and the theory of Diophantine equati…