Do orally

Find remainder when the expression ( 201 8 2018 2018^{2018} -1)( 201 8 2018 2018^{2018} )( 201 8 2018 + 1 2018^{2018} +1 ) + ( 201 9 2019 2019^{2019} )( 201 9 2019 + 1 2019^{2019} +1 )( 201 9 2019 + 2 2019^{2019} +2 ) + ( 202 0 2020 + 1 2020^{2020} +1 )( 202 0 2020 + 2 2020^{2020} +2 )( 202 0 2020 + 3 2020^{2020} +3 ). Is divided by 6


The answer is 0.

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1 solution

Patrick Corn
Dec 4, 2017

The product of three consecutive integers is always divisible by 6 : 6: at least one of them is even and at least one of them is divisible by 3. 3.

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