Problem

Source: American Mathematical Monthly

Tags: linear algebra, matrix, number theory proposed, number theory



Given a prime number p congruent to 1 modulo 5 such that 2p+1 is also prime, show that there exists a matrix of 0s and 1s containing exactly 4p (respectively, 4p+2) 1s no sub-matrix of which contains exactly 2p (respectively, 2p+1) 1s.