In the ring Z[V5], the element 3+ V5 is O Irreducible O reducible O prime O unit

Prove the binomial theorem over any ring R. That is for any a, b E R and positive integer n ≥ 1, (a + b)² = [ (") a² j=0 a²f-j You may use the indentity (=))+ (7) = C) for any j = 0, 1, 2,..., n.

Zp= {0, 1,...,p – 1}, where p is a prime number, is a field under modular addition and modular multiplication. This means that every non- zero element of Zo is invertible. What is the multiplicative inverse of 7 in Z13? Select one: O a. 2 O b. 91 O c. 1 O d. 1/7 O e. 6

Abstract algebra 2 college level