Antimorph
A number which can be represented both in the form x_0^2-Dy_0^2 and in the form Dx_1^2-y_1^2. This is only possible when the Pell equation
| x^2-Dy^2=-1 |
(1)
|
is solvable. Then
x^2-Dy^2 = -(x_0-Dy_0^2)(x_n^2-Dy_n^2)
(2)
= D(x_0y_n-y_0x_n)^2-(x_0x_n-Dy_0y_n)^2.
(3)
See also
Idoneal Number, PolymorphExplore with Wolfram|Alpha
WolframAlpha
References
Beiler, A. H. Recreations in the Theory of Numbers: The Queen of Mathematical Entertains. New York: Dover, 1964.Referenced on Wolfram|Alpha
AntimorphCite this as:
Weisstein, Eric W. "Antimorph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Antimorph.html