1 - 10 of 23 articles
This paper presents a direct and simple approach to obtaining the formulas forS
+ ... +n
wheren andk are nonnegative integers. A functional equation is written based on the functional properties ofS
(n) and several methods of solution are presented. These lead to several...
A quasigroupQ is a set together with a binary operation which satisfies the condition that any two elements of the equationxy =z uniquely determines the third. A quasigroup is in indempotent when any elementx satisfies the indentityxx =x. Several types of Tactical Systems are defined as...
The structure of all distributive topological groupoidsM on a closed or half-closed real interval is completely determined provided one endpoint is a zero forM, M contains an injective idempotent e, and (ex)(ye)= (ey)(xe) holds for allx, y inM. A groupoid is distributive if (xy)z = (xz)(yz)...
In this paper, we discuss the pairs (f, h) of arithmetical functions satisfying the functional equation in the title, whereF is the product off andh under the Dirichlet convolution; that is,F(n) = Σ
ƒ(d)h(n/d) andS(m n) = Σd|(m, n) ƒ(d)h(n/d). The well-known Hölder's identity is a special...
A simple proof by functional equations is given for Ramanujan’s1
1 sum. Ramanujan’s sum is a useful extension of Jacobi's triple product formula, and has recently become important in the treatment of certain orthogonal polynomials defined by basic hypergeometric series.
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