论文标题
乘法函数可通过二进制二进制表单$ x^2 \ pm xy + y^2 $可通勤
Multiplicative functions commutable with binary quadratic forms $x^2 \pm xy + y^2$
论文作者
论文摘要
如果乘法函数$ f $可通勤使用二次表格$ x^2+xy+y^2 $，即\ [f（x^2+xy+y^2）= f（x）^2+f（x）\，f（y）+f（y）+f（y）+f（y）+f（y）+f（y）^2，然后$ f $是$ f $是标识函数。另一方面，如果$ f $可以使用二次表格$ x^2-xy+y^2 $上下班，则$ f $是三种功能之一：身份函数，常数函数和$ \ mathbb {n} \ setMinus p \ setMinus p \ setMinus p \ setMinus p \ setMinus p \ sethbb {n} $。
If a multiplicative function $f$ is commutable with a quadratic form $x^2+xy+y^2$, i.e., \[ f(x^2+xy+y^2) = f(x)^2 + f(x)\,f(y) + f(y)^2, \] then $f$ is the identity function. In other hand, if $f$ is commutable with a quadratic form $x^2-xy+y^2$, then $f$ is one of three kinds of functions: the identity function, the constant function, and an indicator function for $\mathbb{N}\setminus p\mathbb{N}$ with a prime $p$.
