MA-410 Theory of Numbers Spring 2010 Harrelson 201, MW 10:15-11:30am

## Current Announcements

• I have submitted the final course grades (anonymous sorted list) to the registrar. The anonymous sorted grades for the final exam, Final/sorted_grades.txt. The anonymous sorted grades for the combined homeworks scaled to 20, Homework/sorted_grades.txt.
• On request, solution to Homework 4, Problem 1:
```(b0 + 5*b1 + 25*b2)^2 equiv 94 (mod 125). (*)

Then b0^2 equiv 4 (mod 5), so b0 = 2 or = 3.  Take 2.

Then (2 + 5*b1)^2 equiv 94 (mod 25), reducing (*) modulo 25.
So 4 + 4*5*b1 equiv 19 (mod 25), or 20*b1 equiv 15 (mod 25).
That means that 4*b1 equiv 3 (mod 5) [note the division by 5]
or b1 = 2.

Thus (12 + 25*b3)^2 equiv 94 (mod 125) or 144 + 2*12*25*b3 equiv 94 (mod 125).
So 12*50*b2 equiv 94-19 equiv 75 (mod 125).
That means 12*2*b2 equiv 3 (mod 5) [note the division by 25]
or b3 = 2.
```
• The final exam is Wednesday, May 5, at 9am in our class room. You may bring 3 sheets of notes.
• The course web sites for Spring 2009, Spring 2008, Spring 2007 and Spring 2005 contain old homeworks, mid-semester exams, and anonymous grade lists.
• My office hours are listed on my schedule.

 This semester's first and second midterm examinations and final examination (for dates see syllabus) Homework 1, due Monday, Feb. 8 at 4:59pm, in my mailbox in SAS 3151. Homework 2, due Wednesday, Mar 10, at 4:59pm, in my mailbox in SAS 3151. Homework 3, due Mon, Apr 19, 4:59pm, in my mailbox in SAS 3151. Homework 4, due Wed, Apr 28, 4:59pm, in my mailbox in SAS 3151. Web resources for the course Maple basic lesson from MA 141 Victor Shoup's downloadable book A Computational Introduction to Number Theory and Algebra

## Old Announcements

• I have added a hint to the last problem of homework 4.
• Homework 4 is posted. Due last day of class.
• Reema pointed out after class on Wednesday that Taher ElGamal, the inventor of discrete log based public key cryptography, is an Egyptian immigrant. He obtained his undergraduate education in Cairo and his PhD in 1984 from Stanford under the supervision of Martin Hellman.
• Homework 3 is posted. Due Monday, April 19.