The remainder, when 7^ 103 is divided by 17 is ........... - Vidyadip

MCQ

The remainder, when $7^{103}$ is divided by $17$ is $..........$.

A
$11$
✓
$12$
C
$13$
D
$14$

✓

Answer

Correct option: B.

$12$

b
$7^{103}=7 \times 7^{102}$

$=7 \times(49)^{51}$

$=7 \times(51-2)^{51}$

Remainder :- $7 \times(-2)^{51}$

$\Rightarrow-7\left(2^3 \cdot(16)^{12}\right)$

$\Rightarrow-56(17-1)^{12}$

$\text { Remainder }=-56 \times(-1)^{12}=-56+68=12$

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