Four tuple/Modulus of differences/25/Exercise

We consider the mapping

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

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

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

Find an example of a four tuple ${}(a,b,c,d)$ with the property that all iterations ${}\Psi ^{n}(a,b,c,d)$ for ${}n\leq 25$

do not yield the zero tuple. Check your result on http://www.vier-zahlen.bplaced.net/raetsel.php .

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