mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, Heegner's lemma is a lemma used by Kurt Heegner in his paper on the

class number problem In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each ''n'' ≥ 1 a complete list of imaginary quadratic fields \mathbb(\sqrt) (for negative integers ''d'') having c ...

. His lemma states that if :

y^2=a_4x^4+a_3x^3+a_2x^2+a_1x+a_0

is a curve over a field with ''a''₄ not a square, then it has a solution if it has a solution in an

extension Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * E ...

of odd degree.

References

* Diophantine equations Lemmas in number theory {{numtheory-stub