The remainder when ((64) (64) ) (64) is divided by 7 is equal to
Step-by-Step Solution
Key Concept: Use the general term of the binomial expansion for remainder using binomial congruence and impose the required coefficient or exponent condition.
Let$N = ((64)$64 64 ) (2)$N = (64)$2 64 2 64 2$N = (1 + 63)$, let$64 = n$Expanding by binomial n n n 2$N = (1 + 63) = 1$+$C_{1}$63 +$C_{2}$(63) +$\ldots$. =$1 + 6$3$\lambda$=$1 + 7($9$\lambda$) Remainder when divided by 7 is 1
Correct Answer: 2