On a Special Congruence of Carlitz
نویسنده
چکیده
We prove that if q is a power of a prime p and p divides a, with k ≥ 0, then 1 + (q − 1) ∑ 0≤b(q−1)<a ( a b(q − 1) ) ≡ 0 (mod p). The special case of this congruence where q = p was proved by Carlitz in 1953 by means of rather deep properties of the Bernoulli numbers. A more direct approach produces our generalization and several related results.
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