Question

Find the remainder when dividing 2^2013 by 15.

*Answer should be in modulo. Example: Find the remainder when dividing 2^100 by 21 and the answer is 2^100 = 16mod(21).*

Answer 1

$2^{2013}=2^{4\cdot503+1}\\\\2^4=16\equiv 1\pmod{15}\\2^{4\cdot 503}\equiv 1\pmod{15}\\2^{4\cdot 503+1}\equiv 2\pmod{15}\\\\2^{2013}\equiv 2\pmod{15}$