  Given two non-zero integers $a$ and $b$ there exist integers $m$ and $n$ for
which $am-bn =(a,b)$. An increasing number of mathematicians have been calling
this `B\'ezout's identity', some encouraged by finding "identit\'e de B\'ezout"
in Bourbaki's \emph{'El\'ements de math\'ematique}. Moreover the observation
that if $\gcd(a,b)=1$ then this is an `if and only if' condition, is sometimes
called the "Bachet-B\'ezout theorem".
  However this is all in Euclid's work from around 300 B.C., when his writings
are interpreted in context. So why does he not get credit? Some authors learned
the name "B\'ezout's identity" and have perhaps not consulted Euclid, so copied
the misattribution. Others, like some Nicolas Bourbaki collaborators, have
perhaps browsed Euclid's results, but in a form written for the modern
mathematician, and missed out on what he really did (though certainly others,
such as Weil, did not). In this article we will carefully explain what Euclid's
arguments are and what his approach was. We will also share Kowalski's guess as
to the reasons behind Bourbaki's misnomer.
  To appreciate Euclid, you need to read his work in context: Lengths are the
central object of study to the geometer Euclid, though he brilliantly developed
the theory of the numbers that measured those lengths. Today's mathematicians
read his number theory results as being about abstract numbers not
measurements. However the correct interpretation changes how these results are
perceived; Euclid's proofs make clear Euclid's intentions.
  These misperceptions reflect recent discussions about difficulties faced by
indigenous people when learning mathematics. We discuss how some indigenous
groups may learn numbers in certain practical contexts, not as abstract
entities, and struggle when curricula assume that we all share abstract numbers
as a basic, primary fully-absorbed working tool.
