$9*87654321$
Prove that, $9*8765421,98*7654321,987*654321,....98765432*1$are in descending order.
My solution was exactly like that!Phlembac Adib Hasan wrote:Here we are asked to prove $n^5-n\equiv 0(mod\; 10)$.Notice that $n^5-n$ is always even(So it is divisible by $2$) and by Fermat's Little Theorem, it is also divisible by $5$.So we are done.