theorem
  for n be prime Nat holds n divides a|^(n+k) - a|^(k+1)
  proof
    let n be prime Nat;
    a|^(n+k) - a|^(k+1) = a|^n *a|^k - a|^(k+1) by NEWTON:8
    .= a|^n * a|^k - a|^k *a by NEWTON:6
    .= a|^k*(a|^n - a);
    hence thesis by Th58,INT_2:2;
  end;
