Q139 / 200 · Manipal (MET) 2011 · Mathematics

The least remainder when $17^{30}$ is divided by 5 , is

  • A
    2
  • B
    1
  • Correct answer
    C
    4
  • D
    3

Solution

$\begin{aligned} & (17)^2=289 \equiv(-1)(\bmod 5) \\ & \Rightarrow \quad\left(17^2\right)^{15} \equiv(-1)^{15}(\bmod 5)\end{aligned}$ $\begin{array}{ll}\Rightarrow & 17^{30} \equiv-(\bmod 5) \\ \text { i.e., } & 17^{30} \equiv 4(\bmod 5)\end{array}$

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

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