Hi guys if you still take a look here and there at this blog! There is a cool math widget on the igoogle site if you have a google account, and use Igoogle as your homepage, you can search for "math" or "nick's math" and you will get great challenge problems to play with. I have been having fun playing with the following one...
Puzzle 159: Eight odd squares
Lagrange's Four-Square Theorem states that every positive integer can be written as the sum of at most four squares. For example, 6 = 2^2 + 1^2 + 1^2 is the sum of three squares. Given this theorem, prove that any positive multiple of 8 can be written as the sum of eight odd squares.
...I can prove that every odd square is a multiple of 8 +1, and show a few initial cases of odd squares adding up to consecutive multiples of 8, but still working on how to prove that every multiple of 8 can be written as the sum of eight odd squares.
Feel free to give it a try and show me what you have gotten!
