A covering system whose smallest modulus is 40

TextPaul Erdős, in 1950, asked whether for each positive integer N there exists a finite set of congruence classes, with distinct moduli, covering the integers, whose smallest modulus is N  . In this vein, we construct a covering system of the integers with smallest modulus N=40N=40.VideoFor a video summary of this paper, please visit http://www.youtube.com/watch?v=3ev1YjVl0RY.