My math teaser suggestion

[ramse...@msn.com]

I am retired but grew up loving math teasers.  I was a US Patent examiner in Alexandria and retired as a GS-14 primary examiner  I got my start in the Patent Office without any college degree because my appitude for math and machinery allow me to score highly on a appitude test for a trainee program involving both work and study to get an equivalent of a BS degree. My grade school math teacher was an inspiration to me and I would like to contribute to this group in order to return the favor. I think a bright math student in algebra may appreciate the my group on triangular and fibonacci numbers where I posted some teaser that involve the use of algebra to verify some interesting facts about these series.  I am willing to spend a couple of hours a week answering posts and questions about them.  However there are only4 listed members of my group and only one ever responded but is inactive now.  I think that many interesting observations can be made about these series to arouse a greater curiosity about math in grade school.

 

For instance there are triangular numbers that are also square numbers.  I generalized this fact to show that there are an infinite nymber of triangular numbers of the form (x+A)*(x-A)  where x is any number in a particular recursive series of the form S(n) = 6*S(n-1) - S(n-2) and A is a constant integer.  If S(0) = 0 and S(1) = 1 then A equals 0 and the triangular numbers are the square triangular numbers.  For any constant integer A, the starting pair S(0) and S(1) depend on A. The math behind this involves simple algebra. Anyone interested in my ideas please contact me  Ramse...@msn.com