Since infinitely many prime numbers split completely in any number field, there are infinitely many Carmichael ideals in O K {\displaystyle {\mathcal {O}}_{K}} .
Mivel bármely számtestben végtelen sok prímszám bomlik fel teljesen, ezért O K {\displaystyle {\mathcal {O}}_{K}} -ban végtelen sok Carmichael-ideál létezik.