Question

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

• A. 1
• B. 48
• C. none of these

Answer 1

The correct option is C none of these

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)