Adrien-Marie Legendre prime number theorem Dirichlet's theorem on arithmetic progressions Peter Gustav Lejeune Dirichlet Sophie Germain quadratic forms arithmetic
Adrien-Marie Legendre (1752–1833) was the first to state the law of quadratic reciprocity. He also conjectured what amounts to the prime number theorem and Dirichlet's theorem on arithmetic progressions. He gave a full treatment of the equation 



a

x

2


+
b

y

2


+
c

z

2


=
0


{\displaystyle ax^{2}+by^{2}+cz^{2}=0}

 and worked on quadratic forms along the lines later developed fully by Gauss. In his old age, he was the first to prove Fermat's Last Theorem for 



n
=
5


{\displaystyle n=5}

 (completing work by Peter Gustav Lejeune Dirichlet, and crediting both him and Sophie Germain).
