Methods related to the quadratic sieve approach for integer factorization may be used to collect relations between prime numbers in the number field generated by and to combine these relations to find a product representation of this type. The resulting algorithm for solving Pell's equation is more efficient than the continued fraction method, though it still takes more than polynomial time. Under the assumption of the generalized Riemann hypothesis, it can be shown to take time where N = log n is the input size, similarly to the quadratic sieve.
Methods related to the quadratic sieve approach for integer factorization may be used to collect relations between prime numbers in the number field generated by and to combine these relations to find a product representation of this type The resulting algorithm for solving Pell's equation is more efficient than the continued fraction method, though it still takes more than polynomial time Under the assumption of the generalized Riemann hypothesis, it can be shown to take time where N = log n is the input size, similarly to the quadratic sieve