Department of Mathematics

Topical Seminar for Undergraduate Mathematicians

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

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.

 

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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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