A Short Proof of Jacobi's Formula for the Number of Representations of   an Integer as a Sum of Four Squares
  A short and elementary proof, and a finite-form generalization, are given of Jacobi's formula for the number of ways of writing an integer as a sum of four squares (that implies Lagrange's famous 1777 theorem.) 
George Andrews (Pennsylvania State University), Shalsoh B. Ekhad   (Temple University), and Doron Zeilberger (Temple University)