I have a Vivitar 75-205mm 1:3.8 close focusing auto zoom. I'm not a photographer and I would like to know if it can work with a Nikon D3100. On the ring (bottom) it's written "patents applied for N/Ai Lens made in Japan".
The N/Ai indicates that it's a Nikon AI mount lens. This does fit your D3100. There are some caveats listed on the Nikon compatibility chart linked.
But, to summarize, yes - it should mount and work (as well as an old manual lens can be expected to work).