Department of Mathematics

Topical Seminar for Undergraduate Mathematicians

  •  Sum of four squares
  •  12/01/2017
  •  4:10 PM - 5:00 PM
  •  B122 Wells Hall
  •  Rajesh Kulkarni, Mathematics, MSU

A theorem of Fermat and Girard (proved by Euler) states that a positive integer can be written as a sum of two squares if and only if no prime of the form 4k +3 occurs in its prime factorization with odd power. We will discuss a short proof of this due to Zagier. We will then discuss an analogous theorem of Lagrange that proves that every positive integer is a sum of four squares. We will discuss an elementary proof and time permitting, another proof using quaternions.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

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