全国初中数学竞赛和全国各省市的数学竞赛已进行了多年,诞生了许多令人回味无穷的试题,在各类期刊上均有公布,但有些期刊提供的解法比较繁琐.本文给出一些有名的初中数学竞赛试题的简解,供参考.题一(中等数学初中数学奥林匹克训练题)是否存在正整数a、b使得等式a3+(a+b)2+b=b3+a+2成立,如果存在,求出a、b的值,如果不存在,请说明理由. The national junior high school math competitions and math competitions in various provinces and cities across the country have been going on for many years. Many memorable questions have been produced and published in various journals. However, some journals provide solutions that are cumbersome. This article gives some famous ones. A brief explanation of the junior high school math contest questions, for reference. Question 1 (medium mathematics junior high school mathematics olympics) whether there is a positive integer a, b such that the equation a3+(a+b)2+b=b3+a+2 holds if Exist, find the value of a, b, if it does not exist, please explain the reason.