Question

Find the remainder when $7^{55}$ is divided by 29.

• A. 4
• B. 25
• C. 1
• D. 0

Answer 1

The correct option is B

25

We need to use reverse of Euler's theorem as the Euler's number for 29=28.

And the question reduces to $\left(\frac{7^{27}}{29}\right)$ (Rem).

The right answer multiplied by 7, should give a remainder of 1 when divided by 29, as $\left(\frac{7^{28}}{29}\right)$ (Rem) = 1.

Thus, the answer is option (b).

Verification -

25 or $(-4)\times 7$= -28 $⟹$ remainder of 1.