45th Eötvös Competition Problems 1941

1.  Prove that (1+x)(1+x2)(1+x4) ... (1+x2n-1) = 1 + x + x2 + x3 + ... + x2n-1. 2.  The a parallelogram has its vertices at lattice points and there is at least one other lattice point inside the parallelogram or on its sides. Show that its area is greater than 1.