- Homework #1. Practice : 1.3 # 3, 9, 11, 13; 1.5 # 5, 7, 11, 23, 29, 33
Problems due Fri. Sept. 1 : 1.3 # 12, 20; 1.5 # 8, 24, 28
- Homework #2. Practice : 3.3 # 1, 3, 5, 21 ; 3.4 # 1, 3
Problems due Fri. Sept. 8 : 3.3 # 6, 14(a), 22; 3.4 # 4 (c);
Extra credit: 3.3 # 14 (b).
- Homework #3. Practice : 3.1 \# 1, 3, 5, 7; 3.5 \# 1, 5, 13, 31, 33
Problems due Fri. Sept. 15 : 3.1 # 6; 3.5 \# 4, 10, 14, 32
Extra credit (20 points; turn in Friday, Sept. 15):
Consider the statement: Suppose a,b,c,d,e,f are positive
numbers with a/b+c/d=e/f, (a,b)=1, (c,d)=1,
and (e,f)=1. If b doesn't divide d and d doesn't divide b, then f=[b,d].
If this is true, give a proof. If it is false, give a
counterexample, and find stronger conditions on b and d that when
inserted into the statement, make it true (with a complete proof).
- Homework #4. Practice : 3.5 # 41, 43; 3.7 # 1, 9 ; 4.1 # 3, 5, 7,
14, 17, 23
Problems due Fri. Sept. 22 : 3.5 # 60; 3.7 # 2 (b)(c) ; 4.1 # 8, 10, 16, 22
- Homework #5. Practice : 4.2 # 1, 7, 11; 4.3 # 3, 5, 11, 15, 17
Problems due Fri. Sept. 29 : 4.2 # 6, 12; 4.3 # 10, 20(b), 30
Extra credit (turn in Friday, Sept. 29):
3.2 # 22, 24; 3.5 #38, 48, 71
- Homework #6. Practice : 6.1 # 3, 5, 7, 11, 17, 19, 31, 39;
6.3 # 1, 7, 9, 17
Problems due Fri. Oct. 6 : 6.1 # 8, 14, 22, 30; 6.3 # 6, 10
- Homework #7. Practice : 6.3 #17; 7.1 #5
Problems due Fri. Oct. 13 : 7.1 # 2 (b-e), 6, 16
Extra credit (turn in Friday, Oct. 27):
4.3 # 32; 6.1 #42 (use 4.3 #32, not #30 as stated in the problem);
7.1 #26; 9.1 #18; 9.2 #14;
- Homework #8. Practice : 6.2 # 1, 5, 7, 11(a), 16 (a-f)
Problems due Fri. Oct. 20 : 6.2 # 2, 8, 18
- Homework #9. Practice : 9.1 # 1, 3, 7, 9, 15; 9.2 # 1, 3, 7
Problems due Fri. Oct. 27 : 9.1 # 6, 14, 16; 9.2 # 8, 16
- Homework #10. Practice : 9.3 # 1, 3, 5; 9.4 # 19; 9.5 # 5; 9.6 # 1, 3, 9
Problems due Fri. Nov. 3 : 9.3 # 12; 9.4 # 9, 10; 9.6 # 4 (e,f).
Hints: on 9.4 # 9, ignore the solution in
the back of the book (no credit will be given for that method).
Use Theorem 6.13 from class instead. On 9.4 # 10,
use Q=(2p_1 p_2 ... p_n)^4+1 instead of what is written in the book.
Extra credit (turn in Nov. 17) . 9.5 # 6; 9.6 # 8;
(A) Use the method from 9.4 #10 to prove that form every positive
integer m, there are infinitely many primes of the form 2mk+1;
(B) Prove that if (m,n)>1, then (i) σ(mn)<σ(m)σ(n); (ii)
φ(mn)>φ(m)φ(n); (iii) &tau(mn)<&tau(m)&tau(n).
- Homework #11. Practice : 7.1 # 44, 47; 7.2 # 1, 7, 9, 11, 20, 21;
7.3 # 3, 7, 9, 11, 13
Problems due Fri. Nov. 10 : 7.1 # 46; 7.2 # 4, 12, 22; 7.3 # 8, 12
- Homework #12. Practice : 11.1 # 1-5, 8
Problems due Fri. Nov. 17 : 7.4 #30; 11.1 # 6, 14
- Homework #13. Practice : 11.2 # 1, 3, 5
Problems due Fri. Dec. 1 : 11.1 # 44; 11.2 # 2, 4, 6
Extra Credit: 11.1 # 28