Chapter

The Heritage of Thales

Part of the series Undergraduate Texts in Mathematics pp 207-209

Quaternions Applied to Number Theory

  • W. S. AnglinAffiliated withDepartment of Mathematics and Statistics, McGill University
  • , J. LambekAffiliated withDepartment of Mathematics and Statistics, McGill University

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Abstract

In this chapter we shall use integer quaternions to show that every natural number is a sum of four perfect squares. This was first proved by J. L. Lagrange in 1770 (Oeuvres, Vol. 3, pp. 189-201).