
theorem :: Problem 136 Remark
  PrimeDivisors (75) = PrimeDivisors (1215) &
    PrimeDivisors (75 + 1) = PrimeDivisors (1215 + 1)
  proof
A1: PrimeDivisors (75) = PrimeDivisors (3*25)
     .= PrimeDivisors (3) \/ PrimeDivisors (5*5) by DivisorsMulti
     .= PrimeDivisors 3 \/ PrimeDivisors 3 \/ PrimeDivisors 5
          by DivSquare
     .= PrimeDivisors 3 \/ (PrimeDivisors 3 \/ PrimeDivisors 5) by XBOOLE_1:4
     .= PrimeDivisors (5 * 3) \/ PrimeDivisors 3 by DivisorsMulti
     .= PrimeDivisors (5 * 3) \/ PrimeDivisors (3 * 3) by DivSquare
     .= PrimeDivisors (5 * 3) \/ PrimeDivisors (9 * 9) by DivSquare
     .= PrimeDivisors (5 * 3 * (9 * 9)) by DivisorsMulti
     .= PrimeDivisors (1215);
    PrimeDivisors (75 + 1) = PrimeDivisors (2 * 2 * 19)
       .= PrimeDivisors (2 * 2) \/ PrimeDivisors 19 by DivisorsMulti
       .= PrimeDivisors 2 \/ PrimeDivisors 2 \/ PrimeDivisors 19
             by DivisorsMulti
       .= PrimeDivisors (2*2) \/ PrimeDivisors 2 \/ PrimeDivisors 19
             by DivSquare
       .= PrimeDivisors 19 \/ PrimeDivisors (2*2*2) by DivisorsMulti
       .= PrimeDivisors 19 \/ PrimeDivisors (8 * 8) by DivSquare
       .= PrimeDivisors (19 * (8 * 8)) by DivisorsMulti
       .= PrimeDivisors (1215 + 1);
    hence thesis by A1;
  end;
