Mathematics Homework Solutions

Fibonacci Sequence

Please see the attached file for the fully formatted problems.

Rings

See attached (1 and 5) Let R be the 4-element ring...

Fibonacci Sequence

Please see the attached file for the fully formatted problems.

Algebraic Number Theory

Let p be a prime and let a and b be integers...(see attached)

Algebaic Number Theory

Determine if the congruence has solutions....determine the complete solution (see attached)

Finance : Expected Return and Risk

Emery, Finnerty & Stowe - Ch. 6, problems A6, B6, & B10 (a only)- A6. (Expected portfolio return) Musumeci Capital Management has invested its portfolio as shown here. What is Musumeci’s expected portfolio return? B6. (Expected return and risk) Procter & Gamble is considering three possible capital investment ...continues

Algebraic Number Theory

See attached If z=1+3i and w=-3+4i, calculate the values....

Problem in Algorithms

lg stands for log(base 2). For each function f(n) and time t in the attached table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds.

Complex solutions

Determine all complex numbers z such that z^4 + (1 + 8i)z^2 + 8i = 0. Plot your solutions on the complex plane.

Unique Factorization

Use unique factorization in Z[sqrt(-2)] to show that if p is an odd prime and -2 is a square modulo p, then there are integers a and b so that a^2 + 2b^2=p.

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