reserve a,b,c,k,m,n for Nat;
reserve i,j,x,y for Integer;
reserve p,q for Prime;
reserve r,s for Real;

theorem Th59:
  i is even implies i^2 mod 8 = 0 or i^2 mod 8 = 4
  proof
    assume i is even;
    then ex j st i = 2*j by ABIAN:11;
    hence thesis by Lm15;
  end;
