Kronecker's congruence

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Short description: Theorem on a polynomial involving the elliptic modular function

In mathematics, Kronecker's congruence, introduced by Kronecker, states that

Φp(x,y)(xyp)(xpy)modp,

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

Φn(x,j)=τ(xj(τ))

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

References