Reading Quiz Section 3.2
1. True or False: gcd(−21, −12) = −3.
2. Suppose that a = 0. Then gcd(a, 0) is equal to which number?
(a) 0
(b) 1
(c) a
(d) |a|
3. The sequence of remainders produced by the Euclidean algorithm when computing gcd(m, n)
(select all that apply):
(a) is decreasing
(b) is increasing
(c) has all non-negative terms
(d) is infinite
4. True or False: If a and b are relatively prime then the equation ax + by = 1 has an integer
solution (x, y).
Practice Problems Section 3.2
1. Use the Euclidean algorithm to compute gcd( 260, 816) and find integers x, y such that
260x + 816y = gcd( 260, 816)
Video Solution
2. Find solutions to the congruence 5x ≡ 1 (mod 6).
Video Solution
3. Find all integer points on the line 225x + 120y = 15.
Video Solution
4. Suppose a, b, c ∈ Z are such that a and b are relatively prime, a | c, and b | c. Show ab | c.
Video Solution
