The paper [Polynomial-Time Quantum Algorithms for Pell's Equation and the Principal Ideal Problem](http://www.cse.psu.edu/~hallgren/pell.pdf) claims >There are reductions from factoring to solving Pell’s equation, and from solving Pell’s equation to solving the principal ideal problem [BW89b] Can't find their reference [BW89b] on the internet and the extended abstract found doesn't address the issue. What is the reduction from factoring to solving Pell equation? The motivation is that solving the Pell equation $x^2-d y^2=1$ is tractable for $d$ a Fermat number (and possibly for $d=a^2+1$). Experimentally in the above cases the period of the continued fraction for $\sqrt{d}$ is $1$.