what is the remainder when 2^144 is divided by 6? (detailed approach using euler's theorem plz)

Divide both by 2 => Required remainder = 2*(2^143 mod 3)

Euler of 3 = 3*(1-1/3) = 2

So, 2^2 mod 3 = 1

=> 2^142 mod 3 = 1

=> 2^143 mod 3 = 1 * 2 = 2

So, required final remainder = 2*2 = 4