11 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…
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…
Sparse Polynomial GCD Cannot Be Computed in Fixed-output Polynomial Time
Ruichen Qiu, Yichuan Cao, Qiao-Long Huang +2
This paper shows that, assuming , sparse univariate polynomial GCD cannot be computed in fixed-output polynomial time over any fixed computable field. Pre…
Sparse Polynomial Divisibility Test over Finite Field is CoNP-hard
Yichuan Cao, Ruichen Qiu, Qiao-Long Huang +2
In this paper, we show that deciding whether a sparse polynomial does not divide another sparse polynomial exactly over finite fields is NP-hard under BPP many-one reductions. Equi…
A Finite Certificate for the Positive Vasc Inequality
Dakai Guo, Ruichen Qiu, Yichuan Cao +1
We prove the positive-real case of the Vasc cyclic inequality. The proof was obtained with human-guided assistance from the AI agent MechMath Agent Team: the human-readable p…
MechMath: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving
Ruichen Qiu, Yichuan Cao, Junqi Liu +4
Recent advances in large language models (LLMs) and LLM-based agents have substantially improved the capabilities of automated theorem proving. However, for problems that require c…
Hilbert's Irreducibility Theorem for Linear Differential Operators
Ruyong Feng, Zewang Guo, Wei Lu
We prove a differential analogue of Hilbert's irreducibility theorem. Let be a linear differential operator with coefficients in that is irreducibl…
Rational Solutions of First Order Algebraic Ordinary Differential Equations
Shuang Feng, Li-Yong Shen
Let be an irreducible first order ordinary differential equation with polynomial coefficients. Eremenko in 1998 proved that there exists a c…
Rational Solutions of First Order Algebraic Ordinary Differential Equations
Ruyong Feng, Shuang Feng
Let be a first order ordinary differential equation with polynomial coefficients. Eremenko in 1999 proved that there exists a constant …