reserve a,b,k,m,n,s for Nat;
reserve c,c1,c2,c3 for Complex;
reserve i,j,z for Integer;
reserve p for Prime;
reserve x for object;

theorem Th6:
  n * m mod 4 = 1 implies n mod 4 = 1 or n mod 4 = 3
proof
  assume that
A1: n * m mod 4 = 1 and
A2: n mod 4 <> 1 & n mod 4 <> 3;
    n mod (3+1) = 0 or ... or n mod (3+1) = 3 by NUMBER03:11;
    hence thesis by A1,A2,Th5;
  end;
