Belousov问题的解
Solution of Belousov's problem
摘要：
证明了由方程$n$ = F（x_1，.，x_n）= [f_1（x_1）+. + f_n（x_n）]/[x_1 + ... + x_n]，其中f_i（x_i），i，j = 1，.，n是任意函数，是不可约的当且仅当任意两个函数f_i（x_i）和f_j（x_j），i \neq j不都是线性齐次的，或者这些函数是线性齐次的但f_i（x_i）/x_i \neq f_j（x_j）/x_j.这给出了Belousov问题的一个解决方案，构造了任意n个\geq的不可约$n$-拟群的例子3.
英文摘要：
The authors prove that a local $n$-quasigroup defined by the equation x_{n+1} = F (x_1, ..., x_n) = [f_1 (x_1) + ... + f_n (x_n)]/[x_1 + ... + x_n], where f_i (x_i), i, j = 1, ..., n, are arbitrary functions, is irreducible if and only if any two functions f_i (x_i) and f_j (x_j), i \neq j, are not both linear homogeneous, or these functions are linear homogeneous but f_i (x_i)/x_i \neq f_j (x_j)/x_j. This gives a solution of Belousov's problem to construct examples of irreducible $n$-quasigroups for any n \geq 3.
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