MathDB

Let

n

and

k

be positive integers. Consider

n

infinite arithmetic progressions of nonnegative integers with the property that among any

k

consecutive nonnegative integers, at least one of

k

integers belongs to one of the

n

arithmetic progressions. Let

d_1,d_2,\ldots,d_n

denote the differences of the arithmetic progressions, and let

d=\min\{d_1,d_2,\ldots,d_n\}

. In terms of

n

and

k

, what is the maximum possible value of

d

Problem Statement