Need books/articles with proofs of polygonal number theorem

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SUMMARY

The discussion centers on Fermat's polygonal number theorem, which states that any number can be expressed as the sum of n n-gonal numbers. Key references include Nathanson's "Additive Number Theory" and Stillwell's "Mathematics and Its History." The theorem was originally proved by Cauchy in 1813, with a more elementary proof provided by Nathanson in 1987. The user seeks additional resources that offer both historical context and accessible proofs.

PREREQUISITES
  • Understanding of polygonal numbers
  • Familiarity with basic number theory concepts
  • Knowledge of mathematical proofs
  • Access to academic resources or libraries
NEXT STEPS
  • Research "Fermat's polygonal number theorem" for detailed explanations
  • Read Nathanson's "Additive Number Theory" for foundational insights
  • Explore Cauchy's original proof from 1813 for historical context
  • Investigate elementary proofs of number theory theorems
USEFUL FOR

Students, educators, and researchers interested in number theory, particularly those seeking to understand polygonal numbers and their historical proofs.

Wretchosoft
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I am giving a short presentation on Fermat's polygonal number theorem (any number may be written as the sum of n n-gonal numbers). I need books that provide some exposition/history on the theorem as well as a proof. I acquired Nathanson's Additive Number Theory from my university's library, but I'm not sure where to find more on the subject.

Oh, and the proofs should preferably be elementary, as I really know no number theory at all.
 
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Wow, quite a coincidence - I just read chapter 3 of Stillwell, "Mathematics and Its History", which mentions this result! He says it was proved by Cauchy in 1813, with a "short" proof by Nathanson in 1987 (Proc Am Math Soc, 99, 22-24).

good luck!
 

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