Kummer’s Lemma
نویسنده
چکیده
(c0 + c1ζ + · · ·+ cp−2ζ) ≡ c0 + c1 + · · ·+ cp−2 mod p. The number p is not prime in Z[ζ], as (p) = (1 − ζ)p−1, so congruence mod p is much stronger than congruence mod 1− ζ, where all classes have integer representatives. Of course not every element of Z[ζ] that is congruent to a rational integer mod p is a pth power, but Kummer discovered a case when this converse statement is true, for certain primes and certain algebraic integers.
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