Number System
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Q.

The remainder when $7^84$ is divided by 342 is

 A.

0

 B.

1

 C.

49

 D.

241

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Solution:
Option(B) is correct

Solution:

$\dfrac{7^{84}}{342} = \dfrac{(7^3)^{28}}{342}$

$= \dfrac{(343+1)^{28}}{342}$

According to the remainder theorem it will have the remainder = 1.

Edit: For an alternative solution using 'modulus' method, check comment by Sravan Reddy.


(2) Comment(s)


Sravan Reddy
 ()

Using 'modulus' method

7^3 = 343mod342 = (-1)mod342

raising each sides by power 28

(7^3)^28=(-1)^28mod 342

7^84 = 1mod342

reminder = 1


Sravan Reddy
 ()

Sorry, it's not (-1), it should be +1