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arXiv · 2606.12130

Sparse Polynomial Divisibility Test over Finite Field is CoNP-hard

Yichuan Cao·Ruichen Qiu·Qiao-Long Huang·Ruyong Feng·Xiao-Shan Gao
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Abstract

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. Equivalently, the sparse polynomial divisibility test over finite fields is CoNP-hard. This resolves the long-standing open problem concerning the computational complexity of the divisibility test for sparse polynomials in the setting of finite fields.

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Yichuan Cao, Ruichen Qiu, Qiao-Long Huang, Ruyong Feng, Xiao-Shan Gao. 2026-06-10. Sparse Polynomial Divisibility Test over Finite Field is CoNP-hard. https://arxiv.org/abs/2606.12130

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