Observations regarding the repetition of the last digits of a tetration of generic base
Observations regarding the repetition of the last digits of a tetration of generic base
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关于通用碱基四联最后数字重复的观察
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发表时间：
2021
期刊：
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通讯作者：
Luca Onnis
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作者：
Luca Onnis
本文研究了一般基的四分之一[1]的最后一位数的行为。事实上，从某个超指数开始，四次运算的最后一位数字是相同的，为了计算它们，我们将这些表达式约简为mod 10 n。非常令人惊讶的是（尽管未经证明），我认为重复的数字取决于基数的余数模10和一种特殊方式来表达该基数的指数。然后我将讨论结果，我将展示不同的表格和例子来支持我的猜想。1.定义（Tetration）。在数学中，四次方是一种基于迭代或重复求幂的运算。它是在求幂之后，但在pentation之前的下一个超运算。这个词是由Reuben Louis Goodstein从tetra（four）和iteration中创造出来的。n表示n的第a个四次方，或：n n n. } a乘以定义（下限和上限函数）。[2]在数学和计算机科学中，地板函数（floor function）是一个函数，它以一个真实的数x作为输入，并给出一个小于或等于x的最大整数作为输出，记为x x x。类似地，ceiling函数将x映射到大于或等于x的最小整数，表示为x。2.设fq（x，y，n）是一个函数，使得如果：fq（x，y，n）= u则：
This paper investigates the behavior of the last digits of a tetration [1]of generic base. In fact, last digits of a tetration are the same starting from a certain hyperexponent and in order to compute them we reduce those expressions mod 10n. Very surprisingly (although unproved) I think that the repeating digits depend on the residue mod 10 of the base and on the exponents of a particular way to express that base. Then I’ll discuss about the results and I’ll show different tables and examples in order to support my conjecture. 1. DEFINITIONS Definition (Tetration). In mathematics, tetration is an operation based on iterated, or repeated, exponentiation. It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra(four) and iteration. n represent the a-th tetration of n , or: n n n ... } a times Definition (Floor and Ceiling function). [2] In mathematics and computer science, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋. Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉. 2. MAIN CONJECTURE Let fq(x, y, n) be a function such that if: fq(x, y, n) = u Then: