For Monday, October 3rd

For Monday:

  1. Compare to solutions to last daily post.
  2. True fact:  $16080 = 127^2 – 7^2$.  Without doing any factoring or computations besides a bit of adding and subtracting, factor $16080$ as a product of two integers.  (Hint on discord if you are stuck.)
  3. Demonstrate the p-1 factoring method on $n=5063$.  Show the structure of the calculation, but you can use Sage for modular exponentiation, gcd’s, and division.  (You can write a little Sage for-loop to do this, but write up the results in such a way that it demonstrates the method.)
  4. Try to demonstrate the p-1 factoring method for $n=5963$.  It won’t work… what goes wrong?
  5. Why did the last example fail?  Can you design another $n$ for which this method fails?