3
votes
1answer
313 views

Proving conditions on $(r+s)^2 \mid (4r^4+1)$, related to Pell oblongs

While working on another problem (Solving the quartic equation $r^4 + 4r^3s - 6r^2s^2 - 4rs^3 + s^4 = 1$), I came across a question which seems to be of [semi-] independent interest. Conjecture. If ...
5
votes
3answers
1k views

Reduction from factoring to solving Pell equation

The paper Polynomial-Time Quantum Algorithms for Pell's Equation and the Principal Ideal Problem claims There are reductions from factoring to solving Pell’s equation, and from solving Pell’s ...