reserve m, n for Nat;

theorem Th65:
  for k, n being non zero Nat holds
  k divides n & k is square-free iff k divides Radical n
proof
  let k, n be non zero Nat;
  k divides Radical n implies k divides n & k is square-free
  proof
    assume
A2: k divides Radical n;
    Radical n divides n by Th55;
    hence thesis by A2,Th26,NAT_D:4;
  end;
  hence thesis by Lm5;
end;
