@MISC{PYTHTRIP.MIZ,
  AUTHOR = {Wiedijk, Freek},
  TITLE = {Pythagorean Triples},
  SECTION1 = {Relative Primeness},
  SECTION2 = {Squares},
  SECTION3 = {Distributive Law for HCF},
  SECTION4 = {Unbounded Sets are Infinite},
  SECTION5 = {Pythagorean Triples},
  DAY = {26},
  MONTH = {August},
  YEAR = {2001},
  ADDRESS1 = {University of Nijmegen},
  SUMMARY = {A Pythagorean triple is a set of positive integers
  $\{ a,b,c \}$ with $a^2 + b^2 = c^2$.
  We prove that every Pythagorean triple is of the form
  $$a = n^2 - m^2 \qquad b = 2mn \qquad c = n^2 + m^2$$
  or is a multiple of such a triple.
  Using this characterization we show that for every $n > 2$ there exists
  a Pythagorean triple $X$ with $n\in X$.
  Also we show that even the set of {\em simplified\/} Pythagorean triples
  is infinite.}}

