4 papers
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 the equation has n…
Upper and lower estimates for integer complexity
Sergei Konyagin, Kristina Oganesyan
Let stand for the integer complexity of the number , i.e. for the least number of 's needed to write using arbitrary many additions, multiplications, and parenthe…
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 -ary number system with a set of non-negative i…
On Distinct Angles in the Plane
Sergei V. Konyagin, Jonathan Passant, Misha Rudnev
We prove that if points lie in convex position in the plane then they determine distinct angles, provided that the points do not lie on a common circle. This is d…