73 citations · 128 across the 15 of their papers we have counts for
18 papers
Certifying non-existence of integer points on curves
Bogdan Grechuk, Eugene Go
We present an elementary but powerful method for proving that a two-variable equation has no integer solutions. The method produces quadratic identities which every integer solutio…
On the polynomial values represented by binary quadratic forms
Bogdan Grechuk, Jamal Agbanwa
Many Diophantine equations can be reduced to the question of whether, for a given non-degenerate integral binary quadratic form and a univariate polynomial with integer coe…
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…
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…
StepProof: Step-by-step verification of natural language mathematical proofs
Xiaolin Hu, Qinghua Zhou, Bogdan Grechuk +1
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interfac…
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…