Theorem of Nagell-Lutz

In Mathematical, the theorem of Nagell-Lutz is a result of the equation diophantienne of the elliptic curved . Let us suppose that C , defined by

$y^2\; =\; x^3\; +\; ax^2\; +\; bx\; +\; C\; =\; F\; (X)\; \backslash ,$

either a cubic Courbe Not-singular with the whole coefficients has , B , C , and or D the Discriminant of the Polynôme Cubique F ,

$D\; =\; -4a^3c\; +\; a^2b^2\; +\; 18abc\; -\; 4b^3\; -\; 27c^2\; \backslash ,$.

That is to say P = (X, there) a rational point order Finished on C , for the law of group.

Then X and is whole there; and either there = 0, in this case P is of order two, or divides D there.

Result was named thus in honor of those which discovered it independently, Norwegian Trygve Nagell (1895 - 1988) which published it in 1935, and Elisabeth Lutz (1937).

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