Question

What is the remainder when 2^2018 is divided by 33

Answer 1

2^2018=((2^5)^403)×2^3
=(32^2018)×8
so by applying mod we get -1^2018×8
=8 so remainder is 8
32 = -1mod33
32^2018 = -1^2018mod33
(a=bmodc then a^n = b^nmodc
where a is dividend and b is remainder and c is divisor)