This is considering the Phi function (The Euler Phi Function) (a) Explain why φ(m) is always...

This is considering the Phi function (The Euler Phi Function)

(a) Explain why φ(m) is always even when m ≥3.

(b) φ(m) is rarely a prime number. Find all numbers m so that φ(m) is prime.

I'm solving for part b. From part a, it looks like there is no prime number for phi of m when it's greater than or equal to 3. Now, I notice that Phi of 4 is 2, Phi of 3 is 2, and Phi of 6 is also 2. It looks like 2 is prime so does that mean m = 3, 4, 6 are all the numbers m in which Phi of m is prime? Please let me know if this is correct or post a solution to what the correct answer is to part b.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Part 1A: Why is ρ=8cos(φ) a sphere? (greek symbols are rho and phi). What is its...

Part 1A: Why is ρ=8cos(φ) a sphere? (greek symbols are rho and phi). What is its center and radius? Algebra and trig will be needed. Part 1B: Given a right circular cone of radius R and height H, set up a triple integral in spherical coordinates to determine its volume. (Answer should be 1/3πr^2h) Please clearly outline steps used to solve this problem. I have been stuck for a long time. Thank you in advance!

Explain why preferences ≽ that are induced by a utility function are always complete, reflexive, and...

Explain why preferences ≽ that are induced by a utility function are always complete, reflexive, and transitive.

Using the definition of a young function, prove that the conjugate phi^* of a young function...

Using the definition of a young function, prove that the conjugate phi^* of a young function phi is a young function

Explain why prices are always flexible.

Given a function φ(z) with z = x+iy let U(x, y) = ½ [φ(x+iy) +...

Given a function φ(z) with z = x+iy let U(x, y) = ½ [φ(x+iy) + φ(x-iy)] and V(x, y) = i/2 [φ(x+iy) –φ(x-iy)] A) For φ(z) = z2 find U and V and their induced vector fields E =▼U and F =▼V also show that ▼2U = ▼2V = 0 B) Repeat for f(z) = z3 C) For f(z) = ln z we get U(x, y) = ½ ln (x2+y2) and V(x, y) = arctan (y/x) Find ▼U (electrostatic...

Explain why is euler theory good mathematically but not equally good mechanically. Give one example to...

Explain why is euler theory good mathematically but not equally good mechanically. Give one example to prove your point.

Let φ : R −→ R be a continuous function and X a subset of R...

Let φ : R −→ R be a continuous function and X a subset of R with closure X' such that φ(x) = 1 for any x ∈ X. Prove that φ(x) = 1 for all x ∈ X.'

In all algorithm, always explain how and why they work. ALWAYS, analyze the complexity of your...

In all algorithm, always explain how and why they work. ALWAYS, analyze the complexity of your algorithms. In all algorithms, always try to get the fastest possible. A correct algorithm with slow running time may not get full credit. In all data structures, try to minimize as much as possible the running time of any operation. 1.Show that if a binary tree has a vertex with a single child, then this can not be an optimal Huffman tree. 2. Question...

6.8. Determine φ (m), for m =12,15, 26, according to the definition: Check for each positive...

6.8. Determine φ (m), for m =12,15, 26, according to the definition: Check for each positive integer n smaller m whether gcd(n,m) = 1. (You do not have to apply Euclid’s algorithm.)

what is payday loans? are they always ethical? why or why not? explain. what is usury?

Subjects