What is the least value of p such that
(qp),(q+1p),(q+2p)
is an arithmetic progression for some positive integers p and q satisfying 1≤q≤p−2?
Notation: (NM)=N!(M−N)!M! denotes the binomial coefficient.
Bonus: Is it possible for the following progression
(qp),(q+1p),(q+2p),…,(q+np)
to exist for q+n≤p and n>2?