Question

If 2^2020 + 2021 we divide by 9, how much does the remainder increase?​

Answer 1

Given :  2²⁰²⁰ + 2021  divided by 9

To find :  the remainder

Solution:

2²⁰²⁰ + 2021  divided by 9

2²⁰²⁰  = 2²⁰¹⁹.2

= 2.(2³)⁶⁷³

= 2.8⁶⁷³

= 2(9 - 1)⁶⁷³

remainder for (9 - 1)⁶⁷³   = (-1)⁶⁷³  = - 1

remainder for  2(9 - 1)⁶⁷³ = 2(-1) = - 2

2021 /9  =( 2016 + 5)/9

= 224 + 5/9

Hence remainder = 5

2²⁰²⁰ + 2021  divided by 9

remainder = -2 + 5

= 3

2²⁰²⁰ + 2021  divided by 9  remainder = 3

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