reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  for b,n be non zero Nat, a be non trivial Nat holds
    a |-count (a gcd b) = 1 iff a|^n |-count (a gcd b)|^n = 1
  proof
    let b,n be non zero Nat, a be non trivial Nat;
    a divides b iff a|^n divides b|^n by POWD; then
    a |-count (a gcd b) = 1 iff a|^n |-count (a|^n gcd b|^n) = 1 by CD;
    hence thesis by NEWTON027;
  end;
