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On negative Pell equations: Solvability and unsolvability in integers

2018
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Notes on Number Theory and Discrete Mathematics
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Solvability criteria of negative Pell equations x 2 − dy 2 = −1 have previously been established via calculating the length for the period of the simple continued fraction of argument is based on a binary quadratic relation between u n and u n+1 and properties 1+u 2 n u n+1 ∈ N and 1+u 2 n+1 un ∈ N. Due to the recurrence relation of u n , such d's are easy to be generated by hand calculation and computational mathematics via a class of explicit formulas. Besides, we consider equation x 2 − k(k

doi:10.7546/nntdm.2018.24.3.10-26
fatcat:z5v6clnkare6beiih5xghhwtpq