# Пятница 20.07. Zhi-Wei Sun (Nanjing University): "Problems and Results on Sums of Squares"

Due to the efforts of Fermat, Euler, Legendre and Gauss, it is known what

natural numbers can be written as the sum of two squares or three squares.

Lagrange's four-square theorem proved in 1770 states that each natural

number can be expressed as the sum of four squares.

In the talk we will first review classical results on sums of two or three

or four squares. Then we turn to the speaker's recent discoveries which

refine Lagrange's four-square theorem or the Gauss-Legendre theorem on

sums of three squares.

In particular we will introduce our results refining Lagrange's

four-square theorem as well as some recent conjectures of the speaker one

of which states that any integer greater than one can be written as the

sum of two squares, a power of 3 and a power of 5.