1. What is the QFT of the uniform superposition $\frac{1}{\sqrt{M}} \sum_{j=0}^{M-1}\ |j\rangle$?
2. What irrational is represented by $[1,3,3,3,...]$?
3. There is a server running on annai.cs.colorado.edu port 443. It is simulating Shor's algorithm, as described in class. Connect, using TCP/IP, and give it an $x$ and an exponent (number of qubits) and it will give you a random $\ell$. Please use it to factor the number
26825926351488399110544112048484691246984742691774090660107762225282840929762385037237484102637951592668796347757856945214753994377357682664648613794306195119897925017866009997263150512915863644811383848031675519987679409974919170391509730554029294470146117971727639921754779476671008586376903725402571129
Note: the above number is about 1000 bits long and it likely scrolls off your screen to the right. Please make sure you get the whole thing (it starts with 268259 and ends with 2571129).