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, Kronecker's congruence, introduced by Kronecker, states that :

\Phi_p(x,y)\equiv (x-y^p)(x^p-y)\bmod p,

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

\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

* Modular arithmetic Theorems in number theory {{numtheory-stub