Handouts on Equivalence Relations and Modular Arithmetic for M 325K Spring 2024

---

---

Click on the desired handout name.

---

---

• Solving Simple Congruences
• The Euclidean Algorithm for Finding gcd(a,b)
• Expressing d = gcd(a,b) as d = as + bt

  • Attached: Finding an Inverse of N (mod n)

• Alternate Versions of (Epp's 4th Edition) Example 8.4.4 and Example 8.4.5
• Theorems 8.4.1 and 8.4.3 Summary

  • Attached: Theorems (NIB) 4, 5, 6, and 7

• The Definitions of ( n mod d ) and ( n div d )
• Example Proof to Help with Problem #13 of Sec. 8.2
• The Proof of Lemma 8.3.2
• Notes on the Equivalence Relation: Congruence modulo 3 <======> ( CONG_{(mod 3)})
• The "Punctured Plane Relation R" on A = "The Punctured Plane" is an Equivalence Relation
• Proving Relation Properties (Proof Designs)

---

---