 reserve n,i,k,m for Nat;
 reserve p for Prime;

theorem
  for n being non zero Nat holds
    n = (TSqF n) * (n div TSqF n)
  proof
    let n be non zero Nat;
    TSqF n divides n by MOEBIUS2:53; then
A2: n mod TSqF n = 0 by INT_1:62;
    set i2 = TSqF n;
    n = (n div i2) * i2 + (n mod i2) by INT_1:59
      .= (n div i2) * i2 by A2;
    hence thesis;
  end;
