Binomial theorem for positive integral Index

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Question

$If 7^{103} is divided by 25, then the remainder is$

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Solution

$\begin{aligned} We have, 7^{103} = 7 (49)^{51} = 7 (50 - 1)^{51} \\ = 50 k - 7 = 50 k - 25 + 18 \end{aligned}$
$So, remainder is 18 .$

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