I got an interesting new question, it's about number theory and algebra precalculus. Here is the question:
a positive integer $n$ is called valid if $1^n+2^n+3^n+\dots+m^n$ is divisible by $1+2+3+\dots+m$ for every positive integer $m$.
- Prove that 2013 is valid
- Prove that there are infinite positive integers which are not valid
Every little hint, contribution and recommendation would be very helpful. Sorry for my bad english. Thanks before.