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第28届IMO的第四题是一道关于函数方程的试题：求证不存在函数f：N→N，使得对于每个n∈N，f（f（n））＝n＋1987[1]．沈华老师[2]将上述试题推广为下面的定理：定理1设m为自然数，存在函数f:N→N，使得每个n∈N，均有f（f（n））＝n＋m的充要条件是m为偶数．但其证明有一处小
The fourth question of the 28th IMO is a question about functional equations: Prove that there is no function f:N→N, so that for every n∈N, f(f(n))=n+1987[1]. Shen Hua [2] generalized the above questions to the following theorem: Theorem 1 Let m be a natural number and there exists a function f:N→N so that every n∈N has f(f(n))=n+m The condition is that m is an even number. But it proves to have a small