From the 1 of 8 linked papers with an AI index.
8 papers
A systematic approach to Diophantine equations: open problems
Bogdan Grechuk
The paper gathers a collection of simple‑to‑state polynomial Diophantine equations that remain unsolved, highlighting open problems in integer solutions.
On the polynomial values represented by quadratic forms
Bogdan Grechuk, Jamal Agbanwa
Many Diophantine equations can be reduced to the question of whether, for a given non-degenerate quadratic form and a univariate polynomial with integer coefficients, $P(x)…
On the shortest open cubic equations
Bogdan Grechuk, Ashleigh Ratcliffe
We use cubic reciprocity to prove that the equation has no integer solutions. Prior to this work, it was the shortest cubic equation for which the existence of i…
When fractional quasi p-norms concentrate
Ivan Y. Tyukin, Bogdan Grechuk, Evgeny M. Mirkes +1
Concentration of distances in high dimension is an important factor for the development and design of stable and reliable data analysis algorithms. In this paper, we address the fu…
The Risk Quadrangle in Optimization: An Overview with Recent Results and Extensions
Bogdan Grechuk, Anton Malandii, Terry Rockafellar +1
This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and s…
FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
Elliot Glazer, Ege Erdil, Tamay Besiroglu +21
We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most…