The remainder when ((64)^ (64) )^ (64) is divided by 7 is equal t… - Vidyadip

MCQ

The remainder when $\left((64)^{(64)}\right)^{(64)}$ is divided by 7 is equal to

A
4
B
1
C
3
D
6

✓

Answer

B. 1
Let $\mathrm{N}=\left((64)^{64}\right)^{64}$
$\mathbf{N}=(64)^{64^{2}}$
$\mathbf{N}=(1+63)^{64^{2}}$, let $64^{2}=\mathrm{n}$
Expanding by binomial
$\mathrm{N}=(1+63)^{\mathrm{n}}=1+{ }^{\mathrm{n}} \mathrm{C}_{1} 63+{ }^{\mathrm{n}} \mathrm{C}_{2}(63)^{2}+\ldots .$.
$=1+63 \lambda=1+7(9 \lambda)$
Remainder when divided by 7 is 1

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