S. Konyagin

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20122026

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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…

math.NT2025

Unique expansions in number systems via refinement equations

Sergei V. Konyagin, Vladimir Yu. Protasov, Alexey L. Talambutsa

Using the subdivision schemes theory, we develop a criterion to check if any natural number has at most one representation in the $n$ -ary number system with a set of non-negative i…