PROBLEM OF THE MONTH

September 2005





Congratulations to this month's winner &mdash Roman Kogan!
We received 8 solutions to this month's problem. Three of them are full and correct, but the best explained one is that of Roman. The other submitted works give the right answer. However, they do not prove that there are no other possible representations.
Here is the solution by Roman: [PDF]

Find all representations of the number 2n as a sum of squares of four integers.

Examples:
For n=1, the only representation is
2=12+12+02+02,
up to permutations and sign changes.
For n=2, the only representations are
22=12+12+12+12
and
22=22+02+02+02
up to permutations and sign changes.

This month's prize will be awarded to the best explained, correct solution.



Submit your solution to the Mathematics Undergraduate Office (Math P-142) or electronically to problem@math.sunysb.edu by the due date. Acceptable electronic formats are: PDF, Postscript, DVI, (La)TeX, or just plain text. Please include your name and phone number, or preferably your email address.

Closing date: October 6th at 12 pm.