Instructions:
You may email your notebook as an attachment to me at hknaust@utep.edu. Do only send unevaluated notebooks, do NOT send evaluated notebooks!
Alternatively you may post your notebook on your webpage and let me know that you have done so.

Exercise 3: Perfect Numbers

A perfect number is a positive integer m, such that m equals the sum of its proper divisors. 6 is perfect, since 6=1+2+3. 28 is another perfect number: 28=1+2+4+7+14.

Write a program, which finds all perfect numbers less than 300,000. A quite useful command in this context is "Divisors":

Divisors[28]

Exercise 4: The Cycloid

A chalk mark is put on a bicycle tire. As the bicycle moves along the road, the chalk mark describes a curve known as a cycloid.
Build an animation of the motion of the bicycle wheel and the chalk mark.