# If 2^2009 is divided by 17 , then the remainder is

Solution:

$\\2^4=16 \equiv -1(mod 17)\\ \\\Rightarrow (2^4)^502 \equiv (-1)^502(mod 17)\\ \\\Rightarrow 2^2008\equiv 1(mod 17)\\ \\\Rightarrow 2^2009\equiv =2(mod 17)$

$\\\therefore$ Remainder=2

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