# How Half-a-Million Home PC’s Finally Cracked an “Unsolvable” Math Problem

Many people’s home computers sit idly during the day when homeowners are away at work or school.  Did you know that some organizations allow you to connect your computer to a mainframe so that they can “borrow” bits of your operating power to work on difficult problems?  The Charity Engine is one, and it helped to solve one of history’s great unsolved math problems.

Watch the the first 5 minutes of the Numberphile video embedded above, and then read this brief Popular Mechanics article.

Answer the following questions in a few sentences each:

1.  Describe the “sum of three cubes” problem (aka a “Diophantine equation”).
2.  Explain why some numbers (like 4 or 5) will never be written as a sum of three cubes.  What mathematical property do these numbers share that makes them unwritable in this way?
3. Why are 33 and 42 “special cases” when it comes to Diophantine equations?
4. Explain how long it took computers to finally find a Diophantine solution to 33 and 42.
5. Find any two Diophantine solutions/equations that weren’t shared in the video or the article.