Number Theory and Algebra Summary

Tuesday, July 9, 2002

We were pleasantly surprised today by two alternate solutions to our problem from the previous day (integer sides of triangles providing integer areas). First, an expansion of our earlier solution was given and then, a more general one that gave all possible solutions in a very elegant way.

With that out of the way we turned to some interesting questions that could provide a simplistic entree into some sophisticated mathematics:

What numbers can be made by the sum of two (or more) consecutive integers?
How many ways can they be made?
What are the properties of the sum of consecutive squares?

The solutions to these question involve a survey of some very traditional topics that could lead a class, at any level, far and wide.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.