The last digit of 334n+1,n∈N is

The last digit of $3^{3^{4 n}} + 1, n \in N$ is

A
$^{4} C_{3}$
B
$^{8} C_{7}$
C
8
D
4

Solution:

$∵ 3^{4 n} = 81^{n} = (1 + 80)^{n} = 1 + 80 λ, λ \in N$

$∴ 3^{3^{4 n}} = 3^{1 + 80 λ} = 3 \cdot 3^{80 λ} = 3 \cdot (9)^{40 λ} = 3 (10 - 1)^{40 λ}$

$= 3 (1 + 10 μ) = 3 + 30 μ$

$∴ Last digit of 3^{3^{4 n}} + 1 is 4 .$

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