What is the remainder when 1992 is divided by 92?

Question

What is the remainder when $19^{92}$ is divided by 92?

Options:

A . 0

B . 1

C . 48

D . None of these

Answer: Option D
:
D

Euler’s number of $92 = 92 (1 - \frac{1}{23}) (1 - \frac{1}{2}) = 88$

$\frac{19^{88}}{92} | r \times \frac{19^{4}}{92} | r = 1 \times \frac{49}{92} | r = 49$ (from frequency)

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