论文标题
一致性速度公式
The congruence speed formula
论文作者
论文摘要
我们解决了一些与整数四元$ {^{b} a} $的特殊属性相关的开放问题，这是其一致速度的恒定稳定性的任何足够大的$ b = b（a）$。假设radix- $ 10 $（众所周知的十进制数字系统），我们为一致性速度$ v（a）\ in \ mathbb {n} _0 $ a \ in \ mathbb {n} - n} - \ {0 \ {0 \ {0 \ {0 \ {0 \ {0 \ a）提供了明确的公式。特别是，对于任何给定的$ n \ in \ mathbb {n} $中的任何给定的$ n \，我们证明是最小的$ a $ a $ a $ a $ v（a）= n $的trueripà的猜想。此外，对于任何$ a \ neq 1：a \ not \ equiv 0 \ pmod {10} $，我们显示了无限的许多素数的存在$ p_j：= p_j（v（a））$，因此$ v（p_j）= v（a）$。
We solve a few open problems related to a peculiar property of the integer tetration ${^{b}a}$, which is the constancy of its congruence speed for any sufficiently large $b=b(a)$. Assuming radix-$10$ (the well-known decimal numeral system), we provide an explicit formula for the congruence speed $V(a) \in \mathbb{N}_0$ of any $a \in \mathbb{N}-\{0\}$ that is not a multiple of $10$. In particular, for any given $n \in \mathbb{N}$, we prove to be true Ripà's conjecture on the smallest $a$ such that $V(a)=n$. Moreover, for any $a \neq 1 : a \not\equiv 0 \pmod {10}$, we show the existence of infinitely many prime numbers $p_j:=p_j(V(a))$ such that $V(p_j)=V(a)$.
