13 papers
MechMath Agent Team: LLM Driven Agents for Mathematical Research
Yichuan Cao, Ruichen Qiu, Junqi Liu +5
AI reasoning has become a central focus in contemporary artificial intelligence, largely driven by the success of large language models. However, mathematical research, which is ch…
Deterministic Polynomial-time Exact-root Computation for Sparse Polynomials with Bounded Total Degree
Qiao-Long Huang, Yichuan Cao, Ruichen Qiu +1
We study the problem of deterministically computing the exact root of a sparse polynomial in the multivariate setting. Let $f \in \F[x_1,\ldots,x_n]$ be a nonzero polynomial that i…
Complexity of Low-Degree Skew Polynomial Multiplication over Finite Fields
Ke Ye, Yichuan Cao, Ruichen Qiu
In this note, we study the complexity of multiplication in skew polynomial rings over finite fields. We prove that the product of two elements in of degree…
The Equivalence Problem for Generalized Airy Operators
Yichuan Cao, Ruyong Feng, Yunfei Li +1
In this paper, we establish degree obstructions to the equivalence of generalized Airy operators of the same type. As an application, we answer a question posed by Nicholas M. Katz…
Every Nonnegative Integer Is a Sum of a Triangular, a Pentagonal, and a Heptagonal Number
Yichuan Cao, Dakai Guo, Ruichen Qiu +2
In this paper, it is proved that any nonnegative integer can be written in the following form This settles the…
A Greatest Common Divisor Criterion of Certain Binomial Coefficients
Dakai Guo, Ruichen Qiu, Yichuan Cao +2
The binomial greatest common divisor (gcd) criterion recorded as OEIS A080170 is proven. The criterion also appears as conjecture (17) in Ralf Stephan's list of OEIS conjectures. F…