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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,

http://www.scribd.com/doc/79568882/Mathematics-new-discovery

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.

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17  
This is a straightforward corollary of basic results about finite differences, and I am sure it's been known in some form for centuries. – Qiaochu Yuan Jan 30 '12 at 5:53
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Also, one cannot copyright a theorem. – Zev Chonoles Jan 30 '12 at 5:55
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Might be for the best if you first sent your papers to a more subtle peer review before claiming the discovery of a "new theorem". – Henry Shearman Jan 30 '12 at 6:16
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Isn't this a bit harsh? I think it's nice to see people exploring mathematics by themselves, so I have upvoted this question. @Dhanesh: This is quite familiar and many mathematicians have independently discovered it. I believe I've even seen some papers by Euler where he mentions this. Nowadays, it takes a lot of work to discover something really original, as there are A LOT of mathematicians, and they all have their ideas. (And the simple ideas come to mind much more quickly.) So, I wish you a lot of fun exploring mathematics and learning new stuff, that's what really matters. =) – Dejan Govc Jan 30 '12 at 16:15
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-18, seriously? Am I missing something or is that really how we think about an honest attempt at mathematical creativity...? o.O – Myself Jan 30 '12 at 23:25
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closed as not a real question by Asaf Karagila, Listing, Chris Taylor, J. M., jspecter Jan 30 '12 at 14:47

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

1 Answer

up vote 6 down vote

As Qiaochu said in the comments, all of these results follow very straightforwardly from standard, basic results on finite differences. It is possible that no one has ever written them down in exactly this form before, but they are not new in any significant sense. I would not be surprised, for example, to find the first result given as a straightforward exercise in an undergraduate textbook.

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