- Thread starter flamengo
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These are usually auxiliary statements shaped to fit in the specific situation given and thus not very valuable in general contexts.But I think that sometimes it's necessary to prove a new theorem or lemma in order to solve a problem or exercise. Is this true ? I think this occurs mainly in math competitions.

There are mainly two types of theorems in textbooks: those which reveal a deeper understanding of a theory and apply to several situations and those needed to prove them, which are often called lemma or proposition. However, there is no norm of how to call what. Some lemmas do actually belong to the first kind and are still called lemma, e.g. for historical reasons.

In the end you could construct any formula that applies to certain numbers and call it theorem. I once found the following funny formula on the internet: ##2^n+7^n+8^n+18^n+19^n+24^n=3^n+4^n+12^n+14^n+22^n+23^n \; (n=0,\ldots,5)##

I can't imagine anyone who would call it a theorem or even a proposition. And if it can be found in a textbook, then for the same reason as here: for entertainment.

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A method of generating similar formulas for even larger n ranges (but with prefactors) is discussed in this thread.In the end you could construct any formula that applies to certain numbers and call it theorem. I once found the following funny formula on the internet: ##2^n+7^n+8^n+18^n+19^n+24^n=3^n+4^n+12^n+14^n+22^n+23^n \; (n=0,\ldots,5)##

I can't imagine anyone who would call it a theorem or even a proposition. And if it can be found in a textbook, then for the same reason as here: for entertainment.

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