find remainder when 2^1000 is divided by 3
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Given : 2¹⁰⁰⁰ is divided by 3
To Find : Remainder
Solution:
2¹⁰⁰⁰
= ( 3 - 1)¹⁰⁰⁰
All terms will be divisible by 3 except last term which will be
(-1)¹⁰⁰⁰ = 1
Hence remainder = 1
remainder when 2^1000 is divided by 3 is 1
2ⁿ divided by 3
remainder is 1 we n is even
remainder is 2 if n is odd
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