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}`