
theorem KPN:
  for n,k be Nat, p be Prime st k < p holds
    ((n*p + k) choose (n*p)) mod p = 1
  proof
    let n,k be Nat, p be Prime such that
    A1: k < p;
    ((n*p + k) choose k) mod p = 1 by A1,NPK;
    hence thesis by N20;
  end;
