A Short Proof of a Theorem of Pan and Zhang

Xiangyu Wang

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arXiv · 2609.37508

A Short Proof of a Theorem of Pan and Zhang

Xiangyu Wang

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Abstract

Pan and Zhang proved that a positive proportion of positive integers can be represented in the form $a^2+b^2+2^{c^2}$, where $(a,b,c)$ are nonnegative integers. In this note, we give a short proof of their result. The proof uses Romanoff's method and an elementary divisor argument to control the relevant second moment.

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Xiangyu Wang. 2026-09-28. A Short Proof of a Theorem of Pan and Zhang. https://arxiv.org/abs/2609.37508

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