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;

theorem
  b|^2 = a*(a-b) implies 3 divides a & 3 divides b
  proof
    assume b|^2 = a*(a-b); then
    0 = b|^2 - a*a + a*b
     .= b|^2 - a|^2 + a*b by NEWTON:81
     .= (b-a)*(b+a) + a*b by NEWTON01:1; then
    3 divides (b-a)*(b+a) + a*b by INT_2:12;
    hence thesis by Th51;
  end;
