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Aratati ca numarul a=2^2016+2^2017+2^2018+2^2019+2^2020+2^2021 este divizibil cu 7​

Răspuns :

a=2^2016+2^2017+2^2018+2^2019+2^2020+2^2021

= 2^2016(1 + 2 + 2^2 + 2^3 + 2^4 + 2^5)

= 2^2016(1 + 2 + 4 + 8 + 16 + 32)

= 2^2016×63

= 2^2016×9×7 ⋮  7

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