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