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/volume2/exercise7.tex",3 "problem_type": "calculation",4 "problem": "问题27 定义在正整数集 $\\mathbf{N}_{+}$上的函数 $f$ 满足 $f(1)=1$, 且对任意正整数 $m$ 、 $n$, 有\n$$\nf(m)+f(n)=f(m+n)-m n .\n$$\n求 $f$.",5 "solution": "在(1)中令 $n=1$, 得 $f(m)+f(1)=f(m+1)-m$, 即 $f(m+1)- f(m)=m+1$. 于是有 $f(m)-f(m-1)=m, f(m-1)-f(m-2)=m- 1, \\cdots, f(2)-f(1)=2$. 将上面这 $m-1$ 个等式相加, 得 $f(m)-f(1)=2+ 3+\\cdots+m$, 所以 $f(m)=\\frac{m(m+1)}{2}$. 经检验, $f(m)=\\frac{m(m+1)}{2}$ 是原方程的解.",6 "remark": "",7 "figures": []8}