18.1.4. Find all the units, irreducibles, and primes in the ring (Z/10Z, +, ·).

6. Let | En+1 = Cen|En-1. The ansatz |En+1 = ken|P results in √3+1 2 O √3-1 2 Op= √5 +1 2 O √5-1 2 7. Which of the following is a sixth root of unity? O i O-i 01/1/0 + NICO 2.

5.2.2 Prove by induction that for each natural number n, we have 2 = 2"+1 – 1. j=0

6. Show that 2n is O(3n) but that 3n is not O(2n).

14. What are the coefficients of xy20 and x¹7y9 in the expansion of (5x-y) 25?

2.1.3. If a, b are integers such that a = b (mod p) for every positive prime p, prove that a = b.