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在1963年第7期的数学通报上刊登了吳方同志的“化三角为方形”一文,提出了关于不定方程n(n+1)/2=m~2的解法問題,本文介紹一个新的方法。求不定方程 x_(?)(x+1)/2=y~2的一切自然数解的問題相当于求不定方程 x~2+x-2y~2=0 (1)的一切自然数解(为叙述方便起見,下面举凡“自然数解”一律写为“解”)。首先,我們注意到x_1=1,y_1=1是方程(1)的解,下面我們証明不定方程(1)的所有自然数解皆可由
In the 7th issue of the 1963 issue of the Mathematics Bulletin, Comrade Wu Fang published the article “The Triangle Is a Square,” and proposed the solution to the indefinite equation n(n+1)/2=m~2. This paper introduces a new method. The problem of solving all natural number solutions of the indefinite equation x_(?)(x+1)/2=y~2 is equivalent to solving all natural number solutions of the indefinite equation x~2+x-2y~2=0(1) (for narration For convenience, the following “natural number solutions” are all written as “solutions”). First of all, we notice that x_1=1 and y_1=1 are the solutions of equation (1). Next we prove that all natural number solutions of the indefinite equation (1) can be