MathDB

Let

\begin{array}{cccc}a_{1,1}& a_{1,2}& a_{1,3}& \dots \\ a_{2,1}& a_{2,2}& a_{2,3}& \dots \\ a_{3,1}& a_{3,2}& a_{3,3}& \dots \\ \vdots & \vdots & \vdots & \ddots \end{array}

be a doubly infinite array of positive integers, and suppose each positive integer appears exactly eight times in the array. Prove that

a_{m,n}> mn

for some pair of positive integers

(m,n)

12