Saturday, May 23, 2009
JSH: Negative Pell's Equation existence conditions
The existence conditions for non-zero integer solution to j^2 - Dk^2 = -1, are:
There may be more, but probably not.
- For every odd prime factor p of D, p = 1 mod 4.
- If D-1 has 8 as a factor it must have 16 as a factor as well.
- D cannot equal 1 mod 5.
- If D is divisible by 2 it cannot be divisible by 4.
There may be more, but probably not.
# posted by James Harris @ 15:01 
