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What is the tens digit of $17^{1993}?$

 Jun 28, 2021
 #1
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The tens digit is 3

 Jun 28, 2021
 #2
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According to WolframAlpha: https://www.wolframalpha.com/input/?i=17%5E1993

 

The tens digit is 9

 Jun 28, 2021
 #3
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What is the tens digit of 171993?

 

171993(mod100)(172)996+1(mod100)(172)99617(mod100)172=289898910011(mod100)(11)99617(mod100)((11)2)49817(mod100)(121)49817(mod100)|12121(mod100)(21)49817(mod100)(21)599+317(mod100)(215)9921317(mod100)|21501(mod100)(1)9921317(mod100)21317(mod100)157437(mod100)37(mod100)

 

The tens digit is 3

 

laugh

 Jun 28, 2021
edited by heureka  Jun 28, 2021

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