29 Apr
2006
29 Apr
'06
1:34 a.m.
On Fri, 28 Apr 2006, Steve Gray wrote:
... On these scores, e^(i pi)+1=0 is unbeatable.
I am sure that I am missing here something. What is the definition of e^(x+iy) ? Isn't it e^(x+iy)=e^x (cos y + i sin y) ?
Emeric
Hmm. It's been a long time, but my recollection is that the definition of e^z for z complex is that it is the (necessarily unique) analytic continuation of e^x for x real. Another great theorem is that every prime congruent to 1 modulo 4 is a sum of squares in an essentially unique way. But my favorite is that for D > 0, D an integer, not a square, x^2 - Dy^2 = 1 has a solution in integers. John Robertson