p = 4 + 2² + 2³ + 2⁴ + ... + 2²⁰

=> 2p = 8 + 2³ + 2⁴ +2⁵ +  ... + 2²¹

=> 2p - p = (8 + 2²¹) - (4 + 2²)

=> p = 2²¹

So, p can be written as a power of 2

4 + 22 + 23 + 24 + ... + 220

we have:

22 + 23 + 24 + ... + 220 have 220 - 22 + 1 = 199

And the number of even number are:

\(\left(\text{220 - 20}\right):2+1=102\) [even number]

So the number of odd are:

199 - 102 = 97 [odd]

Because the number of odd is a odd 

=> Their sum are a odd

So 22 + 23 + ... + 220 is a odd

P is a odd

So P can't written as power of 2