Bogdan Grechuk

works on

diophantine equations 1 integer solutions 1 open problems 1 polynomial equations 1 unsolved problems 1

From the 1 of 8 linked papers with an AI index.

most citedFrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI

9 citations · 9 across the 6 of their papers we have counts for

collaborators

Showing math.GMShow all

3 papers · 1 filter

math.GM2026

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.

math.GM2026

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 $F$ and a univariate polynomial $P$ with integer coefficients, $P(x)…

math.GM2026

On the shortest open cubic equations

Bogdan Grechuk, Ashleigh Ratcliffe

We use cubic reciprocity to prove that the equation $7 x^{3} + 2 y^{3} = 3 z^{2} + 1$ has no integer solutions. Prior to this work, it was the shortest cubic equation for which the existence of i…