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On divisibility of one special type of numbers. (English) Zbl 1029.11004
The main results established in this paper are concerned with divisibility of the numbers
\( ((k+1)^n- nk-1)/k^2 \), where \(k\) is any positive integer and \(n\) is any nonnegative integer. These numbers are related to those studied by the same authors in a previous paper [Tatra Mt. Math. Publ. 20, 75-85 (2000; Zbl 0992.11025)]. The binomial theorem plays a central role in the proofs. Some remarks are made concerning the primality of the considered numbers.
MSC:
11A51 Factorization; primality
11A07 Congruences; primitive roots; residue systems
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References:
[1] Seibert J., Trojovský P.: On some properties of one special type of polynomials and numbers. Tatra Mountains Mathematical Publications · Zbl 0992.11025
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