Could someone check to see if I got this right. It says 'divisible' not 'evenly divisible'. I think it proves divisibility. And is there a difference between 'divisible by ' and 'factor of'? they seem to be the same thing.

is divisible by if . For all positive integers n.

1. first I prove n=1 is true.

2. then I assume n=k is true and solve for (k+1)th item.