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 Th68:
  3|^(2*k),1 are_congruent_mod 4
  proof
    (2*4+1) mod 4 = 1 mod 4 by NAT_D:21
    .= 1 by NAT_D:24;
    then 3|^2,1 are_congruent_mod 4 by Lm8;
    then 3|^2|^k,1|^k are_congruent_mod 4 by GR_CY_3:34;
    hence 3|^(2*k),1 are_congruent_mod 4 by NEWTON:9;
  end;
