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