math-ai/BlueMO
BlueMO 🚀 BlueMO: A Comprehensive Collection of Challenging Mathematical Olympiad Problems from the Little Blue Book Series BlueMO is a comprehensive and challenging dataset comprising mathematical olympiad problems paired with detailed solutions, meticulously curated from the esteemed "Little Blue Book" (小蓝书) series (Second Edition)—a vital resource for Chinese students training for national and international olympiad math competitions. Designed to… See the full description on the dataset page: https://huggingface.co/datasets/math-ai/BlueMO.
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1{2 "source_file": "./raw_volume-zh/volume1/exercise4.tex",3 "problem_type": "calculation",4 "problem": "问题10 设 $k$ 为正整数, $M_k$ 是 $2 k^2+k$ 与 $2 k^2+3 k$ 之间 (包括这两个数在内) 的所有整数组成的集合.\n能否将 $M_k$ 拆分为两个不相交的子集 $A 、 B$, 使得\n$$\n\\sum_{x \\in A} x^2=\\sum_{x \\in B} x^2 ?\n$$",5 "solution": "当 $k=1$ 时, $3^2+4^2=5^2$; 当 $k=2$ 时, $10^2+11^2+12^2=13^2+14^2$. 猜想: $M_k$ 中前 $k+1$ 个数的平方和与后 $k$ 个数的平方和相等.",6 "remark": "",7 "figures": []8}