Question

Aratati ca numarul A=2²⁰²⁰+2²⁰²¹+2²⁰²²+2²⁰²³ este divizibil cu 30​

Answer 1

${2}^{2020} + {2}^{2021} + {2}^{2022} + {2}^{2023} = {2}^{2020} (1 + 2 + {2}^{2} + {2}^{3} ) = {2}^{2020} (1 + 2 + 4 + 8) = {2}^{2020} \times 15 = {2}^{2019} \times 2 \times 15 = {2}^{2019} \times 30$

Answer 2

$a = {2}^{2020} + {2}^{2021} + {2}^{2022} + {2}^{2023} =$

$= {2}^{2020} \times ( {2}^{0} + {2}^{1} + {2}^{2} + {2}^{3} ) =$

$= {2}^{2020} \times (1 + 2 + 4 + 8) =$

$= {2}^{2020} \times 15 =$

$= {2}^{2019} \times {2}^{1} \times 15 =$

$= {2}^{2019} \times 30 = > \: nr. \: a \: este \: divizibil \: cu \: 30$