Difference between revisions of "Talk:Modular arithmetic/Introduction"

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A couple of clocks for modulo 5 and modulo 12 would make a great addition to the early part of this article.--[[User:MCrawford|MCrawford]] 19:35, 28 June 2006 (EDT)
 
A couple of clocks for modulo 5 and modulo 12 would make a great addition to the early part of this article.--[[User:MCrawford|MCrawford]] 19:35, 28 June 2006 (EDT)
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“What is the last digit of <math>(...((7)^7)^7)...)^7</math> if there are 1000 7s as exponents and only one 7 in the middle? We can solve this problem using mods. This can also be stated as <math>7^{7^{1000}}</math>.”
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It seems to me that the expression simplifies to <math>7^{1000}</math>, no?

Latest revision as of 10:02, 17 July 2022

AoPSWiki Article of the Day
Modular arithmetic/Introduction was the AoPSWiki Article of the Day for January 27th, 2008

This page is a small experiment to see if it's a better way to organize an amount of information that is sure to become very large.--MCrawford 16:34, 28 June 2006 (EDT)


A couple of clocks for modulo 5 and modulo 12 would make a great addition to the early part of this article.--MCrawford 19:35, 28 June 2006 (EDT)


“What is the last digit of $(...((7)^7)^7)...)^7$ if there are 1000 7s as exponents and only one 7 in the middle? We can solve this problem using mods. This can also be stated as $7^{7^{1000}}$.”

It seems to me that the expression simplifies to $7^{1000}$, no?