I think I have discovered a new theorem in mathematics.I would like to know whether it's really a discovery. The gist of the discovery is given below. Further the complete paper is available at,
Those who're familiar with "calculus of finite differences" may find some resemblance. However this result is different as "calculus of finite difference" cannot be used for arithmetic progression .
Gist of the Theorem.
The squares of the consecutive elements of an arithmetic progression are in a quadratic series with a specific numerical relation between the common difference of the arithmetic progression and the second difference of the quadratic series , which is Second difference = 2 . square of the common difference of the arithmetic progression.
Further, this is true for any power of the elements of an arithmetic progression such that, **n th difference = n factorial . n th power of the common difference of the arithmetic progression.