MAT3702 Assignment 2 solutions 2026
DUE: 19 AUGUST 2026
ALL QUESTIONS ARE ANSWERED FULLY AND VERIFIED
, Assignment 2
1. Prove:
𝑏 ∣ 𝑎 ⟺ (−𝑏) ∣ 𝑎
Proof:
(⇒ direction)
Assume 𝑏 ∣ 𝑎
Then:
𝑎 = 𝑏𝑘for some 𝑘 ∈ ℤ
Now:
𝑎 = (−𝑏)(−𝑘)
So:
(−𝑏) ∣ 𝑎
(⇐ direction)
Assume (−𝑏) ∣ 𝑎
Then:
𝑎 = (−𝑏)𝑘
𝑎 = 𝑏(−𝑘)
So:
𝑏∣𝑎
Proven.
DUE: 19 AUGUST 2026
ALL QUESTIONS ARE ANSWERED FULLY AND VERIFIED
, Assignment 2
1. Prove:
𝑏 ∣ 𝑎 ⟺ (−𝑏) ∣ 𝑎
Proof:
(⇒ direction)
Assume 𝑏 ∣ 𝑎
Then:
𝑎 = 𝑏𝑘for some 𝑘 ∈ ℤ
Now:
𝑎 = (−𝑏)(−𝑘)
So:
(−𝑏) ∣ 𝑎
(⇐ direction)
Assume (−𝑏) ∣ 𝑎
Then:
𝑎 = (−𝑏)𝑘
𝑎 = 𝑏(−𝑘)
So:
𝑏∣𝑎
Proven.
