Kronecker's congruence - Alchetron, the free social encyclopedia

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

Φ p ( x , y ) ≡ ( x − y p ) ( x p − y ) mod p ,

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

Φ n ( x , j ) = ∏ τ ( x − j ( τ ) )

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

References

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