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A matrix of 0s and 1s

Source: American Mathematical Monthly

April 9, 2012
linear algebramatrixnumber theory proposednumber theory

Problem Statement

Given a prime number pp congruent to 11 modulo 55 such that 2p+12p+1 is also prime, show that there exists a matrix of 00s and 11s containing exactly 4p4p (respectively, 4p+24p+2) 11s no sub-matrix of which contains exactly 2p2p (respectively, 2p+12p+1) 11s.