Multistage Problem 1 Lucas Numbers

To solve this problem you must solve 4 other questions that I have created. The solutions to these problems will give you the information necessary to solve this question. The questions that must be answered before attempting this one can be found in the links below and all of them are calculus problems. The first person to solve this problem will get 10 points, the second person 9 points and so on until the tenth person gets 1 point. I will continue to post multistage problems until someone reaches 50 points and then the leaderboard will refresh and that person will win.

Present Delivery 2.0 Solution = A

Curly Solution = B

Nested Squareroot Solution = C

Another Differentiation Solution = D

Now for the question. Let $A + B + C + D = E$ . A Lucas number is a member of the sequence defined as $L_ {0} = 2$ , $L_{1} =1$ and $L_{n} = L_{n-1} + L_{n-2}$ for $n > 1$ . $E$ happens to be a Lucas number. How many 1's are in the binary representation of $L_{E}$ ?

Please post that you have solved this problem here .