希望数学大佬们有哪个会的讨论一下~
1.存在无穷多个$m \inZ $,使得 \[\varphi (m) = \sigma (m) \]其中:\[ \varphi (m) = m\mathop{\Pi}\limits_{p|m} (1-\frac{1}{p}) \] \[ \sigma (m)= \mathop{\Pi}\limits_{p|m} (1+p+ \dots +p^{\alpha}) \]
2.形如$ p=13k+1 $的素数有无穷多个?
3.(不知道是否正确)判断此命题是否为真命题:
若{$ x_{n} $} $ _{+\infty} $的映射 {$ p | p|x_{n} $ }也是无穷数列,
则{$ x_{n+1} $} $ _{+\infty} $的映射{$ p | p|x_{n+1} $ }也是无穷数列; |