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Compute 35^1723-16^1723 modulo 6.

 Aug 21, 2020
 #1
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(35^1723-16^1723) mod 6 = 1

 Aug 21, 2020
 #2
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35^1723-16^1723

 

\(35^{1723}-16^{1723}\;\;(mod \;6)\\ =(-1)^{1723}-(-2)^{1723}\;\;(mod \;6)\\ =-1--(2)^{1723}\;\;(mod \;6)\\ =-1+2\;\;(mod \;6)\qquad \text{(2 to the power of any odd interger, mod 6, is 2)}\\ =1 \;\;(mod\; 6) \)

 Aug 22, 2020

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