Sum of reciprocals problem

This week we have a new table to make, and it will hopefully contribute to our solution of the problem stated in this week's second threaded discussion.

The problem is: for each integer n > 1, find distinct positive integers x and y such that:

  1     1      1
 ___ + ___ =  ___
   
  x     y      n
(or 1/x + 1/y = 1/n). For example, if n=2, we can choose x=3 and y=6, since 1/3 + 1/6 = 1/2.

So, as we did last week, everyone fill in at least two rows of the following table. This should give us sufficient data to figure out a pattern and solve the problem for any n. Be sure to identify yourself as the author of your rows.

If you have any questions about this, or thoughts that might lead toward the general solution, be sure and post them to the threaded discussion.

As you complete the table, try to type the HTML code directly into the source file -- don't use an HTML composition program like FrontPage.

n x y because Author
2 3 6 1/3 + 1/6 = 1/2 Dr. D
3 4 12 1/4 + 1/12 = 1/3 Dr. D
4 5 20 1/5 + 1/20 = 1/4 Dr. D