reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem
  for k,x,y being Nat st x^2 - 2*y^2 = k
  for t,u being Nat st t = x-2*y & u = x-y holds
  t^2 - 2*u^2 = -k;
