$2009^{2008}$ +$2011^{2010}$ chia hết cho 2010
= $2009^{2008}$+$2011^{2010}$ + 1 - 1
=($2009^{2008}$+ 1) + ($2011^{2010}$– 1)
= (2009 + 1)($2009^{2007}$- …) + (2011 – 1)($2011^{2009}$ + …)
= 2010($2009^{2008}$ - …) + 2010($2011^{2009}$+ …)
⇒ Chia hết cho 2010