Q120 / 170 · Manipal (MET) 2019 · Mathematics

The remainder obtained when $5^{124}$ is divided by 124 is

  • Correct answer
    A
    $5$
  • B
    $0$
  • C
    $2$
  • D
    $1$

Solution

We have, $5^{124}=\left(5^3\right)^{41} \cdot 5$ $\begin{aligned} & \text { Now, } & 5^3 & =1(\bmod 124) \\ & \therefore & \left(5^3\right)^{41} & =1(\bmod 124) \\ & & \left(5^3\right)^{41} \cdot 5 & =1(\bmod 124) \\ \Rightarrow & & 5^{124} & =5(\bmod 124) \end{aligned}$

Hence, the correct answer is option: 'A'.

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