QJEEM23Ma89cd: JEE Main 2023 Mathematics - Class 11 JEEM23Ma89cd Solution: The remainder, when 7 103 is divided by 17, is __________

Question

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

Accepted Answer

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

\begin{aligned} = 7 \times (49)^{51} \\ = 7 \times (51 - 2)^{51} \end{aligned}

Remainder =

7 \times(-2)^{51}

\begin{aligned} = - 7 (2^{3} \cdot (16)^{12}) \\ = - 56 (17 - 1)^{12} \end{aligned}

Remainder

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

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