Show that the composite number 1281 is a strong pseudoprime base 41.
"$n-1=2^rm$, then n is a strong pseudoprime base b if either $b^m=1modn$ or $b^{2^sm}=-1modn$"
Ok so I have $n=1281$ and $b=41$
then $n-1=1281-1=1280=2^8*5$ so $r=8$ and $m=5$
then $b^mmodn=41^5mod1281=1280$
and $b^{2^sm}modn=41^{2*5}mod1281=1$
Where am i making a mistake? Is it just a computational error or am I misunderstanding somehting? Do I need to try more "s" values?