On a generalization of a theorem by Euler

In this paper a natural generalization of a theorem by Euler in 1744 is presented. Extensive searches failed to locate this result in existing literature or in well known mathematical websites such as MathWorld (http://mathworld.wolfram.com), nor could it be derived by using software for analytical computation like Maple. The obtained identity is fascinating and surprisingly simple, and it paves the way for interesting applications.