Under a mild condition, Ryser's Conjecture holds for every n:= 4h^2 with h>1 odd and non square-free

Abstract

We prove, under a mild condition, that there is no circulant Hadamard matrix $H$  with $n >4$ rows when
$\sqrt{n/4}$ is not square-free. The proof introduces a new method to attack
Ryser's Conjecture, that is a long standing difficult conjecture.