Question

The remainder when 2^(2003) is divided by 17

Answer 1

Apply the below given method to solve these types of questions:

2^2003 / 17

Divide the last two digits of the power with 4 as "2" has a cyclicity of 4.

So , 03/4 , rem = 3

Now use this remainder  as s power in 2 = 2^3 = 8

8 /17

Rem = 8 ans

Things to remember

2 , 3 , 7 and 8 has a cyclicity of 4. So whenever you see such a problem divide the last two digit of the power with 4 and then proceed you will get your answer quickly.

Answer 2

hi

Solution:-

___________________________________

2^(2003)/17

2003/4 = reaminder = 3

2 is cyclic

then use this remainder  as s power in 2 = 2^3 = 8

= Rem = 8 ans