reserve a,b,i,k,m,n for Nat;
reserve s,z for non zero Nat;
reserve c for Complex;

theorem Th48:
  not 7 divides a implies a^2 mod 7 = 1 or a^2 mod 7 = 2 or a^2 mod 7 = 4
  proof
    assume not 7 divides a;
    then ex k st a^2 = 7*k+1 or a^2 = 7*k+2 or a^2 = 7*k+4 by Th46;
    hence thesis by Th16;
  end;
