
theorem
  for n,q,b being Nat holds
  q gcd b = 1 & q <> 0 & b <> 0 implies q|^n gcd b = 1
proof
  let n,q,b be Nat;
  assume that
A1: q gcd b = 1 and
A2: q<>0 & b<>0;
  q,b are_coprime by A1,INT_2:def 3;
  then (q|^n),b are_coprime by A2,EULER_2:17;
  hence thesis by INT_2:def 3;
end;
