2^90/91 remainder?

64?

81 is the remainder

Remainder = 64
This question can be done within a minute if you know the application of euler no.
=> If X ^ E(N) / N, where N and X are co-prime then remainder = 1.
X = 2 and N = 91.
E(91) i.e. euler no. of 91= 72.
Therefore 2^72 / 91, remainder = 1
For remaining 2^18 / 91, break 2^18 into [2^6 X 2^6 X 2^6]
so it is 64 X 64 X 64 / 91
=> (-27) X (-27) X (-27) / 91
=> 729 / 91 X (-27) / 91
=> 1 X -27 => -27
Therefore remainder = 64 (i.e 91 -27).