Question on conguence

[filipmark]

Hi all
All numbers invloved are natural and N is a prime other than 2. Symbol "|" means "divides"
It is known that
N^k|a+b → N^k+1| a^N+b^N
Does anyone know if the converse also holds? That is
N^k+1| a^N+b^N → N^k|a+b