A fundamental discriminant is an integer divisible
by any square of any odd prime , and satisfies
The first few positive fundamental discriminants are 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, ... (OEIS A003658 ). Similarly, the
first few negative fundamental discriminants are A003657 ).
For an integer Wolfram
Language test NumberFieldDiscriminant Sqrt [d ]]
== d returns True iff
See also Class Number ,
Dirichlet
L -Series ,
Discriminant ,
Regulator
Explore with Wolfram|Alpha
References Atkin, A. O. L. and Morain, F. "Elliptic Curves and Primality Proving." Math. Comput. 61 , 29-68, 1993. Borwein,
J. M. and Borwein, P. B. Pi
& the AGM: A Study in Analytic Number Theory and Computational Complexity. Cohn, H. Advanced
Number Theory. Dickson, L. E. History
of the Theory of Numbers, Vol. 1: Divisibility and Primality. Dickson, L. E. History
of the Theory of Numbers, Vol. 2: Diophantine Analysis. Dickson, L. E. History
of the Theory of Numbers, Vol. 3: Quadratic and Higher Forms. Sloane, N. J. A. Sequences A003657 /M2332
and A003658 /M3776 in "The On-Line Encyclopedia
of Integer Sequences." Referenced on Wolfram|Alpha Fundamental Discriminant
Cite this as:
Weisstein, Eric W. "Fundamental Discriminant."
From MathWorld https://mathworld.wolfram.com/FundamentalDiscriminant.html
Subject classifications More... Less...
that is not equal to 1, not divisible
by any square of any odd prime, and satisfies 
or 
.
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, ... (OEIS A003657).
other than 1, the Wolfram
Language test NumberFieldDiscriminant[Sqrt[d]]
== d returns True iff 
is a fundamental discriminant.
