MathDB

All perfect squares, and all perfect squares multiplied by two, are written in a row in increasing order. let

f(n)

be the

n

-th number in this sequence. (For instance,

f(1)=1,f(2)=2,f(3)=4,f(4)=8

.) Is there an integer

n

such that all the numbers

f(n),f(2n),f(3n),\dots,f(10n^2)

are perfect squares?

Problem Statement