theorem Th45:
  (a <> 0 or b <> 0) & n > 0 & a divides b|^n - 1 implies a,b are_coprime
  proof
    set g = a gcd b;
    assume (a <> 0 or b <> 0) & n > 0 & a divides b|^n - 1;
    then g divides b|^n & g divides b|^n - 1 by INT_2:2,21,NEWTON02:14;
    then g divides b|^n - (b|^n - 1) by INT_5:1;
    hence thesis by WSIERP_1:15;
  end;
