IIRC Martuuk wanted 300 LY and Farseer wanted Meta Alloys. Meta Alloys can be found in the Pleiades Nebula, which coincidentally is 300 LY out.
So I bought a DBX with an SRV, fuel scoop, ADS and a bit of cargo space, and headed out on what I considered to be a dry run for future exploration trips. I was a bit nervous, having never traveled more than a few jumps to a destination, but it was easy. No problems with endless unscoopable stars.
Check your statistics for the total distance from start on the right hand panel. You can also check to see if this requirement has been unlocked on the same panel, engineers tab at the bottom. Martuuk didn't unlock at exactly 300 LY so I added a couple of jumps over 300 and then it unlocked.
You can also sell your exploration data to both engineers to build rep, after they have been unlocked.