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常见一些确定自然数高次幂末几位数的问题,如确定7~(9803)的末三位数,1986~(2001)的末四位数,4390625~(789)的末五位数等等。1983年第一期《数学通报》已载文论及m~n的末三位数,本文拟就m~n的末k位数作初步探讨,并寻找此类问题的一般规律与简捷解法。一、m~2末k位数的不变性约定本文所用字母均表示非负整数;以〔α〕、{α}分别表示α的整数部分和小数部分;以m_k表示一个k位数,不足k位时,高位用0补齐。如327可表为m_5=00327;以M_k表示一个k位数,它的平方的末k位仍然是
Common problems that determine the number of natural numbers at the end of high power, such as determining the last three digits of 7~(9803), the last four digits of 1986~(2001), the last five digits of 4390625~(789), etc. . In the first issue of “The Mathematics Bulletin” in 1983, the last three digits of m~n were included in this paper. This article intends to make a preliminary discussion on the final k number of m~n and look for the general laws and simple solutions to these problems. First, m ~ 2 at the end of k number of immutable conventions The letters used in this article represent non-negative integers; [α], {α}, respectively, said that the integer part and the decimal part of α; m_k represents a k-digit, less than k When the position is high, the high position is filled with 0. For example, 327 can be expressed as m_5=00327; a k-bit is represented by M_k, and the last k bits of its square are still