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 NEWTON89:
  for a be Integer, m,n be Nat st
    m>=n holds a|^n divides a|^m
  proof
    let a be Integer, m,n be Nat;
A1: |.a|^n.| = |.a.||^n & |.a|^m.| = |.a.||^m by TAYLOR_2:1;
    assume m >= n;
    hence thesis by INT_2:16, A1,NEWTON:89;
  end;
