论文标题
残留类无Euler功能值的值
Residue classes free of values of Euler's function
论文作者
论文摘要
我们表征了哪些残基类包含无限多个量表（Euler函数的值），哪些不包含。我们表明，所有不含基准的残基类别的结合均具有渐近密度3/4，也就是说，几乎所有2 mod 4的数字均在一个不含基本的残基类中。在另一个方向上，我们显示了奇数m的正密度，因此对于任何$ s \ ge0 $和任何偶数$ a $ a $，残基类$ a \ pmod {2^sm} $都包含无限的数量。
We characterize which residue classes contain infinitely many totients (values of Euler's function) and which do not. We show that the union of all residue classes that are totient-free has asymptotic density 3/4, that is, almost all numbers that are 2 mod 4 are in a residue class that is totient-free. In the other direction, we show the existence of a positive density of odd numbers m, such that for any $s\ge0$ and any even number $a$, the residue class $a\pmod{2^sm}$ contains infinitely many totients.
