We give a survey on problems from Number Theory that can be solved or were solved by the methods of Additive
Combinatorics such as Green--Tao theorem, Ostmann conjecture, the distribution of Fermat quotients, exponential sums over multiplicative subgroups, combinatorial problems with continued fractions and so on.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/7671