KGS math club/solution 11 6

Here is a set of relative speeds of the horses, to solve the problem:

1, 1+1/720, 1+1/727, 1+1/728, 1+1/734, 1+1/735, 1+1/740, 1+1/741, 1+1/755

This was provided by iceweasel, who wrote:

This Haskell program

main=mapM_((putStr "slowdowns 1+1/">>).print.head).iterate(>>= (\l->[a:l|a<-[1..headl-1],all(\b->a*(a+1)`mod`(b-a)==0)l])).map(:[])$[1..]

outputs solutions for numbers of horsemen from 2 to 10 slowdowns 1+1/[1]
slowdowns 1+1/[1,2]
slowdowns 1+1/[1,2,3]
slowdowns 1+1/[2,3,4,5]
slowdowns 1+1/[8,9,10,11,12]
slowdowns 1+1/[20,23,24,25,26,27]
slowdowns 1+1/[54,55,56,57,59,60,63]
slowdowns 1+1/[720,727,728,734,735,740,741,755]
slowdowns 1+1/[470280,470287,470294,470295,470300,470301,470303,470304,470315]