How many people are required to maintain genetic diversity?

Inbreeding isn't negative at all, so one couple would suffice for colonization.

Inbreeding fixes recessive traits and the ones displaying unwanted traits can be culled. Actually, inbreeding is one of the most potent weapons of evolution, it speeds things up greatly. We went through a major bottleneck event ourselves and lived to tell the tale.

The exact number of individuals needed for a healthy species that will survive X number of generations depends on the species though. To maintain healthy genetic diversity and establish enough different alleles to allow for sustainability of the species. I don't remember the exact number but I think for humans it was something between 1000 or 10000, and if you get below that number the species will likely go extinct by natural causes.

Of course, everything is completely different when you have full control over who mates with who. But still, in the above example of 1 couple, they can successfully start a seemingly healthy population, but due to low genetic diversity they - as a species - won't be able to respond to, say, increased radiation, changes in atmosphere, a virus, bacteria, shortage of food, etc. That's why 1 couple is basically enough, but to ensure longetivity of the species 25 couples is far from enough.