You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:


Log in to your personal account or through your institution.

New Looks at Old Number Theory

Aimeric Malter, Dierk Schleicher and Don Zagier
The American Mathematical Monthly
Vol. 120, No. 3 (March 2013), pp. 243-264
DOI: 10.4169/amer.math.monthly.120.03.243
Stable URL:
Page Count: 22
  • Download ($19.00)
  • Cite this Item
Item Type
New Looks at Old Number Theory
Preview not available


Abstract We present three results of number theory that all have classical roots, but also modern aspects. We show how to (1) systematically count the rational numbers by iterating a simple function, (2) find a representation of any prime congruent to 1 modulo 4 as a sum of two squares by using simple properties of involutions and pairs of involutions, and (3) find counterexamples to Euler’s conjecture that a fourth power can never be the sum of three fourth powers by using properties of quadratic polynomials with rational coefficients.

Page Thumbnails