Q107 / 170 · Manipal (MET) 2017 · Mathematics

When $5^{20}$ is divided by 7, the remainder is

  • A
    1
  • B
    3
  • Correct answer
    C
    4
  • D
    6

Solution

Now, $5^2 \equiv 4(\bmod 7)$ $\begin{aligned} 5^4 & \equiv 16(\bmod 7)=2(\bmod 7) \\ \left(5^4\right)^5 & \equiv 2^5(\bmod 7) \\ 5^{20} & \equiv 32(\bmod 7)=4(\bmod 7) \end{aligned}$ $\therefore$ Remainder is 4 .

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

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