人类遗忘的难题解法，被GPT-5重新找出来了

Core Insights - The article discusses the resolution of the Erdős problem 339, a significant mathematical challenge that was previously marked as unsolved but was actually resolved in 2003. This was discovered using GPT-5 Pro, which identified the relevant literature through an image of the problem [1][5][7]. Group 1: Erdős Problem 339 - Erdős problem 339 is a classic problem in number theory concerning the existence of a positive lower density for the set of integers that can be expressed as the sum of exactly r distinct elements from a given r-ary basis [2][3]. - The problem was previously thought to be unresolved, but it was confirmed that it had been solved in a paper published in the Journal für die reine und angewandte Mathematik in 2003 [5][6]. Group 2: Community Response - The discovery made by GPT-5 Pro sparked significant interest and discussion among mathematicians and online communities, highlighting the tool's capability in identifying existing solutions to complex problems [1][4][17]. - Various mathematicians engaged in discussions about the implications of the Erdős problem and its connections to other mathematical conjectures, such as Waring's Problem, emphasizing the rigorous conditions of the Erdős problem compared to other cases [3][4]. Group 3: Implications of GPT-5 Pro - The use of GPT-5 Pro in academic research has been praised for its efficiency in identifying flaws in published papers, demonstrating its potential to accelerate the verification of scientific literature [17][18][21]. - Suggestions for optimizing the use of GPT-5 Pro in research include deep reading techniques and circularity audits, which could enhance the process of reviewing scientific documents [21].