Question

the remainder when 2 raise to the power 2019+2020 is divide by 17 is​

Answer 1

Step-by-step explanation:

Remainder of

$\frac{ {2}^{2019} + 2020}{17}$

for this we have to calculate the value of both remainder and add them

$\frac{ {2}^{2019} }{17} \\ \frac{ {2}^{3} \times {2}^{2016} }{17} \\ 6 \times { {2}^{4} }^{54} \div 17 \\ 8 \times {16}^{54} \div 17 \\ 8 \times - 1 = - 8 \\ \\ 17 - 8 = 9 \\ \\ this \: 9 \: is \: adde in \: 2020 \\ 2020 + 9 = 2029 \\ 2029 \div 17 \\ \\ remainder \: is6 \:$