Question

find the remainder when 2 power 2013 is divided by 17 ​

Answer 1

Answer:

2383628.8823529

Step-by-step explanation:

this your answer

Answer 2

Given:

$\bold{\frac{2^{2013}}{17}}$

To prove:

Find the remainder.

Solution:

$\Rightarrow \bold{\frac{2^{2013}}{17}}$

As we know,

$= 2^1 = 2\\\ = 2^2 =4\\\ = 2^3 =8\\.\\.\\.\\.\\\ So, \ = 2^{2013}$ can be written as:

$= \ 2^{2012 \times 2 }$

$= ((2)^{4})^{504} \\\\ = 16^{504}$

$= \frac{16^{504} \times 2 }{17}\\\\= \frac {(16^{504}) \times 2 }{17}}\\\\= (-1)^{504} \times 2 \\\\= 1\times 2 \\\\ = 2$

The remainder to the given value is = 2.