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近年来国内外数学竞赛中,含有特殊定义的问题时有出现。其题型有写出要求符合定义的数(或数组)有多少个,写出符合定义的数或数组等。解答这类问题的关键之一在正确理解题中的特殊概念。特殊定义的含意,并以此为依据进行推理或计算。以下举出三例。例1 (1991年北京市中学生数学竞赛试题)如果能找到自然数a和b,使得n=a+b+ab,则称n为一个“好数”。例如3=1+1+1×1。即3是一个好数。在1～100这些自然数中,“好数”共有多少个? 先观察“好数”的特征:n=a+b+ab。由此可知n+1=a+b+ab+1=(a+1)(b+1)为合
In recent years, problems with special definitions have appeared in mathematic competitions at home and abroad. The question type is to write out how many numbers (or arrays) are required to meet the definition, write a number or array that matches the definition. One of the keys to answering such questions is to correctly understand the special concepts in the questions. The meaning of the special definition, and based on this reasoning or calculation. The following are three examples. Example 1 (1991 Beijing Middle School Students Mathematical Contest Question) If we can find the natural numbers a and b such that n=a+b+ab, then n is said to be a “good number”. For example, 3=1+1+1×1. That is, 3 is a good number. In 1 to 100 of these natural numbers, how many “numbers” are there? First observe the characteristics of “good”: n=a+b+ab. It can be seen that n+1=a+b+ab+1=(a+1)(b+1) is