Four tuple/Modulus of differences/Descent/Exercise

We consider the mapping

$\Psi \colon \mathbb {N} ^{4}\longrightarrow \mathbb {N} ^{4}$

that assigns to a four-tuple ${}(a,b,c,d)$ the four-tuple

$(\vert {b-a}\vert ,\vert {c-b}\vert ,\vert {d-c}\vert ,\vert {a-d}\vert ).$

Show that for any initial value ${}(a,b,c,d)$, after finitely many iterations, this map reaches the zero-tuple.

Create a solution