On 24 Jul 2011, at 22:08, benjayk wrote:

1) show that 1 has 8 clothes. (easy) example of clothes for 1
(1^2+0^2+0^2+0^2, 0^2+1^2+0^2+0^2, (-1)^2+0^2+0^2+0^2, ...)
2) show that 2 has 24 clothes (easy but longer)
3) show that all numbers have clothes (very difficult)
4) well Jacobi result: show that the male's number of clothes is 8
times the number of their divisors, and show that the female's number
of clothes is, well a bit more complex, it is 24 times the number of
their *male* divisors.  (super extremely difficult).
I recall male number = odd number, and female number = even number.

Take it easy. Jacobi' result illustrates beautiful number's pattern.
Its proof lead to the notion of modular form, which are really crazy
object in math, and physics. They play a key role in Wiles proof of
Fermat theorem.

That poetry reminds us that the very little numbers like 0, 1, 2, are
very important.
Interesting. I'm not really interested in mathematical excercise right now. I just finished my exams (including math) and just want to relax from this
stuff ;).

And I just sent two mathematical theories! Apology. Relax. I wish you good Holiday.



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