reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

theorem
  for p be prime Nat holds
    not p divides a|^(2*n+1) + b|^(2*n+1) & p divides a|^2 - b|^2
  implies p divides a - b
  proof
    let p be prime Nat;
    assume not p divides a|^(2*n+1) + b|^(2*n+1) & p divides a|^2 - b|^2; then
    not p divides a + b & p divides (a+b)*(a-b) by NEWTON01:1,Th98;
    hence thesis by INT_5:7;
  end;
