On a class of combinatorial sums involving generalized factorials.

Chou, W.-S.; Hsu, L.C.; Shiue, P.J.-S.

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The article focuses on simple identities found for binomials, their divisibility, and basic inequalities. A general formula allowing factorization of the sum of like powers is introduced and used to prove elementary theorems for natural numbers. Formulas for short multiplication are sometimes referred in English or French as remarkable identities. The same formulas could be found in works concerning polynomial factorization, where there exists no single term for various identities. Their...