Topology of Numbers · Problem 4.3.3

Classification of Quadratic Forms — Allen Hatcher

Mathematics — Number Theory · pells-equation-nonsquare

Problem

Show that every positive integer that is not a square can be expressed as a quotient

n^2 - 1/k^2

for a suitably chosen pair of integers

n

and

k

, and in fact there are infinitely many different choices for such a pair. Why did we exclude squares?