midterm prep don't use for general revision

Question 1

If d | a then |d| ≤ |a|:

Answer 1

false, every integer divides 0 and all are larger lmao

Question 2

c | a and c | b if and only if c | gcd(a, b):

Answer 2

By Bezout’s identity, there exist integers s and t such that gcd(a, b) =
as + bt. Since c | a and c | b if and only if there exist integers e and f
such that a = ce and b = cf , it follows that c | a and c | b if and only if
gcd(a, b) = ces + cf t = c(es + f t)

Question 3

bezout:

Answer 3

gcd(a,b)=as+bt where s and t are integers, to find s,t treat the euclidean algo as equations and a,b as algebra not numbers

Question 4

euclidean algo final answer:

Answer 4

the last remainder that’s not 0 lmao