Math 444/544

Fall 2026

• Syllabus.
• Some resources if you want to learn TeX. Many students like Overleaf.
• Homework 1 (due 10/2):

  §1.1 #1, 2, 5, 6, 7, 9, 10. Optional: 11.

  Solutions: pdf, tex.

• Quiz 1 (10/7):

  1. Let a, b, q, r ∈ ℤ and b > 0. Define what we mean by ”when a is divided by b, the quotient is q and the remainder is r.&squo;

  §1.1 #6: Let a, b, c ∈ ℤ. Suppose that when a is divided by b, the quotient is q and the remainder is r, and that when q is divided by c, the quotient is k and the remainder is s. Prove that when a is divided by bc, the quotient is k.

• Homework 2 (due 10/9):

  §1.2 #1abc, 4b, 9, 12, 13, 17, 22, 25. Optional: 33.

  §1.3 #4, 18, 21.

  Solutions: pdf, tex.

• Quiz 2 (10/14):

  1. State Bézout's lemma (Theorem 1.2).

  §1.2 #25(a): If a, b, u, v ∈ ℤ are such that au + bv = 1, prove that (a,b) = 1.

  (b): Show by example that if au + bv = d > 1, then (a,b) may not be d.

• Homework 3 (due 10/16):

  §1.3 #25, 35a.

  §2.1 #1, 4, 6, 15, 20.

  §14.1 #8, 9. Optional: 19, 20.

  Solutions: pdf, tex.

• Quiz 3 (10/21): /tr>

  1. State Euclid's lemma (Theorem 1.5).

  §2.1 #20(a): if a² ≡ b² (mod n) then a ≡ ± b (mod n).

  (b): Same question when n is prime.

• Homework 4 (due 10/23):

  §3.1 #13, 27, 29, 31, 32. Optional: 44.

  §3.2 #1, 3.