
theorem for a,b be odd Integer, m be even Nat holds
  Parity (a|^m + b|^m) = 2
  proof
    let a,b be odd Integer, m be even Nat;
    reconsider n = m/2 as Nat;
    A1: (a|^n)|^2 = a|^(2*n) & (b|^n)|^2 = b|^(2*n) by NEWTON:9;
    2|^(2|-count ((a|^n)|^2+(b|^n)|^2)) = 2|^1 by NEWTON03:74;
    hence thesis by A1,Def1;
  end;
