Homework 57j
Michael
In homework 57j, the left side of the equation is [[a,b][c,d]]. I'm
wondering if this is a typo or not. Should it be [[a,b],[c,d]] (note
the extra comma, two arguments to the lcm), or as it is in my book
(with only one argument to the lcm)? A one argument lcm seems kinda
pointless to me, unless it's trying to test if we're reading carefully.
If that's the case, um, well, oops... =P
Professor, how would you like us to interpret it?
Thanks,
-Michael
Kenneth A. Ribet
Looks to me as if there's a missing comma, as you say. Anyone in the
class have the original book in Hungarian?
Best,
Ken R
Kenneth A. Ribet
The material that I presented in class today gives perspective to
Theorem 16 on page 28, which I expect to prove on Wednesday. I hope
also to prove on Wednesday or Friday that primes of the form 4k+1 are
sums of two squares. Where in the book do the authors prove this
result? The answer is that it appears as Theorem 13 on page 137; the
authors' proof is very different from the one that I have in mind.
On pages 208-209, the authors use this latter theorem, plus Theorem
16 on page 28, to establish (Theorem 2) the characterization of sums
of two squares that we gave in class today.
See http://en.wikipedia.org/wiki/
Fermat's_theorem_on_sums_of_two_squares for the Wikipedia article
"Fermat's theorem on sums of two squares" and http://en.wikipedia.org/
wiki/Proofs_of_Fermat%27s_theorem_on_sums_of_two_squares for three
proofs of the result. The proof that I'll give is not in the
Wikipedia article.
Best,
Ken R