New posts in Additive Combinatorics

Goldbach conjecture and other problems in additive combinatorics

Does the expression $x^4 +y^4$ take on all values in $\mathbb{Z}/p\mathbb{Z}$?

Size of sets with complete double

$|(A+B)(X)|=o(X)$ if $|A(X)|=O(X^{1/2})$ and $|B(X)|=O(X^{1/2})$?

Sets A such that A+A contains the largest set [0,1,..,t]

Is there a set of positive integers of density 1 which contains no infinite arithmetic progression?

An extremal combinatorics problem

Maximize $f(0)+\cdots+f(n-1)$ subject to $f(x)f(y) + f(x+y) \leq 1$

Is each finite group multifactorizable?

Lagrange four squares theorem