Kronecker's congruence

Template:Short description In mathematics, Kronecker's congruence, introduced by Kronecker, states that

${\mathrm{\Phi }}_p(x,y)\equiv (x-y^p)(x^p-y)modp,$

where p is a prime and Φ_p(x,y) is the modular polynomial of order p, given by

${\mathrm{\Phi }}_n(x,j)=\prod _{\tau }(x-j(\tau ))$

for j the elliptic modular function and τ running through classes of imaginary quadratic integers of discriminant n.

References

• Template:Citation