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Find the last three digits of 101^{202}  \(\phantom{101^101}\)

 Jun 26, 2022
 #1
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+1

101^202 % 10^10==8603030201 - these are the last 10 digits.

 Jun 27, 2022
 #2
avatar+118139 
+1

101 = 1.01e2 = 101

101^2 = 10201

101^3 = 1030301

 

101^9 = 1093685272684360901

 

101^10 = 110462212541120451001

 

We seem to have a pattern here, based on the pattern   the last 3 digits are most likely  201

 Jun 27, 2022

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