Find the remainder when 7 55 is divided by 29. Options: A . &nbsp4 B . &nbsp25 C . &nbsp1 D . &nbsp0 E . &nbsp3q+ r

Find the remainder when 755 is divided by 29.

Question

Find the remainder when

7^{55}

is divided by 29.

Answer: Option B
:
B
We need to use reverse of Euler's theorem as the Euler's number for 29=28.
And the question reduces to

(\frac{7^{27}}{29})

(Rem).
The right answer multiplied by 7, should give a remainder of 1 when divided by 29, as

(\frac{7^{28}}{29})

(Rem) = 1.
Thus, the answer is option (b).
Verification -
25 or

(- 4) \times 7

= -28

⟹

remainder of 1.

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