Need books/articles with proofs of polygonal number theorem

  • Thread starter Thread starter Wretchosoft
  • Start date Start date
  • Tags Tags
    Proofs Theorem
Click For Summary
Fermat's polygonal number theorem states that any number can be expressed as the sum of n n-gonal numbers. For a presentation, resources like Nathanson's "Additive Number Theory" and Stillwell's "Mathematics and Its History" are recommended, as they provide historical context and proofs. Cauchy originally proved the theorem in 1813, with Nathanson offering a more concise proof in 1987. The request emphasizes the need for elementary proofs due to a lack of background in number theory. Finding accessible literature on this theorem will enhance understanding and presentation quality.
Wretchosoft
Messages
64
Reaction score
0
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.
 
Physics news on Phys.org
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!
 
Thread 'How to define a vector field?'
Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...

Similar threads

  • · Replies 12 ·
Replies
12
Views
594
  • · Replies 105 ·
4
Replies
105
Views
8K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K