Power divides?

Find the sum of all positive integers $n$ such that $\displaystyle \sum_{j=0}^n {2n+1 \choose 2j+1 } 2^{3j}$ is divisible by $5$ .

$\Large \color{#3D99F6}{\text{CALVIN, READ HERE ONWARDS} }$

Question(start)

In an alternative universe, our planet Earth is dying and NASA decided to move the entire human civilization to another habitable planet, Edmunds that is 20 lightyears away from Earth via a spacecraft. The good news is that this spacecraft has warp drive which means it can travel faster than the speed of light. However, to minimize fuel consumption, the spacecraft controls the speed at which it is travelling. The rule is that the speed at which it travel is equal to the distance to the destination. How long until it takes for the spacecraft to reach Edmunds ?

Details and Assumptions :

• As an explicit example, if you are 15 lightyears away from Edmunds , then your speed must be 15 lightyears per hour.

• Suspend your disbelief that you can travel faster than the speed of light.

Image Credit: Flickr Sosiaalisesti Rajoittuneet .

Question(end)

Answer choices

We will never reach Edmunds <<< Correct answer
20 years
$\sqrt{20}$ years
1 year
400 years

Logic > Paradoxes > Zeno's Paradox

Level 4 (I believe)

Notes

1. Source .

2. Edmunds is a fictional planet in the flim Interstellar . Have you watched the film? It's awesome! (understatement)

3. Suggested title: "Murph, I love you, forever"