Task: Text Categorization
Input (English): The converse of this theorem is the basis of the Pratt certificate. Paul Zeitz' proof of this theorem relies on considering a bracelet consisting of beads with a fixed number of characters, then removing those with only one unique character. Another proof of it relies on using Lagrage's theorem on a multiplicative group G. Also the basis of the RSA encryption scheme, the Carmichael numbers notably foil the test named for this theorem, which can be generalized using Euler's totient function. Stating that a to the p is congruent to a modulo p, for ten points, identify this theorem of number theory named after a French mathematician, which is less famous than its namesake's last one.
Output (English): Science