7 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…
Output-sensitive Sparse Polynomial GCD over Finite Fields is NP-hard
Ruichen Qiu, Yichuan Cao, Qiao-Long Huang +2
In this paper, we prove that output-sensitive sparse polynomial GCD computation over finite fields is NP-hard under BPP many-one reduction. More precisely, for two sparse univariat…
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…