MATH 235: Assignment 1 solutions
2. Please note that for this problem N must be assumed bigger than 0.
N
N
a) n=1 [n, n] = [N, N ],
n=1 [n, n] = [1, 1].
b) n=1 [n, n + 1] = [1, ),
n=1 (n, n + 2) = (1, ).
c) n=1 (n, n + 1) = (1, )\N,
n=1 (1/n, 1] = (0, 1]
MATH 235: Sample Midterm
(1) Using the Euclidean algorithm, nd d = gcd(144, 55) as well as integers u, v
such that 144u + 55v = d. Use that to solve the equation
[144]x = [3]
in Z/55Z
Solution: Applying the Euclidean Algorithm,
144 = 55 2 + 34
55 = 34 1 +
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