S. Konyagin

activity

20122026

collaborators

Showing 2026Show all

3 papers · 1 filter

math.CO2026

On polynomial expanders with many variables

M. Z. Garaev, S. V. Konyagin

For a fixed integer $n \geq 2,$ we consider the homogeneous polynomial $P (x_{1}, x_{2}, \dots, x_{n + 2}) = i = 1 \sum n (x_{2} - x_{1})^{i - 1} x_{1}^{n - i} x_{i + 2} .$ We prove that, for any fin…

math.NT2026

Upper and lower estimates for integer complexity

Sergei Konyagin, Kristina Oganesyan

Let $∥ n ∥$ stand for the integer complexity of the number $n$ , i.e. for the least number of $1$ 's needed to write $n$ using arbitrary many additions, multiplications, and parenthe…

math.NT2026

On Sidon sets with squares, cubes and quartics in short intervals

M. Z. Garaev, F. M. Garayev, S. V. Konyagin

Representative examples of our results are as follows. For any positive integer $N$ the equation $x^{3} + y^{3} = z^{3} + t^{3}, x, y, z, t \in N, {x, y} \neq = {z, t}$ has n…