Mappings/Table of values/25614377/1003the composition/Exercise

Consider the set ${}M=\{1,2,3,4,5,6,7,8\}$, and the mapping

$\varphi \colon M\longrightarrow M,x\longmapsto \varphi (x),$

defined by the following table

${}x$	${}1$	${}2$	${}3$	${}4$	${}5$	${}6$	${}7$	${}8$
${}\varphi (x)$	${}2$	${}5$	${}6$	${}1$	${}4$	${}3$	${}7$	${}7$

Compute ${}\varphi ^{1003}$, that is, the ${}1003$-rd composition (or iteration) of ${}\varphi$ with itself.

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