The remainder, when 7^ 103 is divided by 23 , is equal to: - Vidyadip

MCQ

The remainder, when $7^{103}$ is divided by 23 , is equal to:

✓
14
B
9
C
17
D
6

✓

Answer

Correct option: A.

14

(A) 14
$
\begin{array}{l}Sol.\
7^{103}=7\left(7^{102}\right)=7(343)^{44}=7(345-2)^{34} \\
7^{103}=23 K_1+7.2^{44} \\
\text { Now } 7.2^{34}=7 \cdot 2^2 \cdot 2^{12} \\
=28 \cdot(256)^4 \\
=28(253+3)^4 \\
\therefore 28 \times 81 \Rightarrow(23+5)(69+12) \\
23 K_2+60 \\
\therefore \text { Remainder }=14
\end{array}
$

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