  In this paper we solve the Diophantine equation
  $\binom{m}{l}-\binom{n}{k}=d$ (where m,n are positive integers unknowns)
  when (k,l)=(3,6) for various values of d and when (k,l)=(8,2) and d=1.
  As a byproduct of our results we will obtain that (k,l)-near collisions with
difference 1 do not exist if (k,l)=(6,3), (3,6), (8,2) thus establishing a
conjecture stated in the article "Binomial collisions and near collisions"
published by A. Blokhuis, A. Brouwer and B. de Weger in Integers 17 (2017),
A64.
