Let M={(x,y)∈R×R:x2+y2≤r2}, where r>0. Consider the geometric progression an=12n−1,n=1,2,3,… . Let S0=0 and, for n≥1, let Sn denote the sum of the first n terms of this progression. For n≥1 let Cn denote the circle with center (Sn−1,0) and radius an and Dn denote the circle with center (Sn−1,Sn−1) and radius an.
Consider M with r=1025513. Let k be the number of all those circles Cn that are inside M. Let l be the maximum possible number of circles among these k circles such that no two circles intersect. Then