Numbers Definition and 1000 Threads

Why are perfect numbers important? What is the best way of introducing these numbers to a first course on number theory? I could not find any application apart from the relation to Mersenne primes. Are there any other applications of perfect numbers?

Hello, I am trying to calculate the surface cooling rate from the sides of a round tin can using Rayleigh, Prandtl and Grashof numbers but I'm getting a ridiculously high result, and I'm hoping someone could run through my numbers to tell me where I'm going wrong. Posting my question is...

I have a list of numbers x = [1, 11, 21, 1211, 111221,...], I need to find the 31st number in that list.

Evaluate the following expressions, expressing answers in rectangular form. 1. $\cos(1+j)$ 2.$\sinh(4-j3)$ can you help me on how to solve these problems. thanks in advance!

for about first 429407636 pi digits where can i get such software or how can i calculate it? (i have 1b pi digits)

Ive had this problem with the calculator since I bought it. It might be that the calculator does not have enough implemented functions to pull it off or I am missing something. It happens when I am solving for imaginery roots. Example: y^2 + y^1+y = 0. I go to mode, and select 6(equation)...

Basically I want to take an unknown amount of variables and sum them up. I'm sure it's simple. I know there is some way to tell VS to keep reading the opened stream from my numbers.txt file. #include <iostream> #include <fstream> using namespace std; ifstream data_input...

We know that i^3 is -i . But I am getting confused, because I thought that i can be written as √(-1) and i^3 = √(-1) × √(-1) × √(-1) = √(-1 × -1 × -1) = √( (-1)^2 × -1) = √(1× -1) = √(-1) = i ( and not -i ). Please help.:rolleyes: Sorry I couldn't use superscript because I was using my phone.

Please forgive me as I may have to edit this post to get the equations to show properly. I am doing some work with AC circuits and part of one of my phasor equations has this in it: \frac {2i} {1+cos(θ) + i sin(θ)} - i , where i is the imaginary number \sqrt{-1}. However, knowing the...

Find the number between 1000 and 2000 that cannot be expressed as sum of (that is >1) consecutive numbers.( To give example of sum of consecutive numbers 101 = 50 + 51 162 = 53 + 54 + 55 ) and show that it cannot be done

Hey again! (Rock)(Wasntme) I want to show that there are infinitely many composite numbers $n$,for which stands: $$a^{n-1} \equiv 1 \pmod n$$ So,it must be: $n \mid a^{n-1}-1$ But how can I show that there are infinitely many such $n$ ?? (Thinking)

Homework Statement My textbook says any integer greater than 1 is a product of primes. Wouldn't that mean that there are no prime numbers? What is the product of primes that create the integer 23? Homework Equations The Attempt at a Solution

Hello! (Wave) I am looking at the following exercise: Find how many numbers $k$ with $1 \leq k \leq 3600$ exist,that have at least one common factor $>1$ with $3600$. I thought that the number we are looking for is equal to: $$3600-\phi(3600)=3600-\phi(2^4 \cdot 3^2 \cdot 5^2...

What's a good book on split-complex numbers? If it also covers dual numbers or the relation between split-complex numbers and special relativity or Minkowski 4-space or some analysis of split-complex numbers then all the better, but that's just gravy. I really just want a good reference for...

is there a way to solve this without performing the tedious expansion of $(1+j)^8$? here's the problem $\text{Im}[(1+j)^8(x+jy)]$

An irrational number is any real number which cannot be expressed as the ratio of two real numbers. Then is 3.62566 is also an irrational number? I thought all irrational numbers are uncountable. I am not sure that the above is an irrational number :confused:

Solved~Rearranging numbers changes answers? Homework Statement A car starts from rest and travels with a constant acceleration of 3ms^{-2}, while a bike which is at a distance of 100m away from the car starts with an initial velocity of 5ms^{-2} travels with a constant acceleration of...

Homework Statement Prove that the set of all algebraic numbers is a countable set. Solution: Algebraic numbers are solutions to polynomial equations of the form a_0 x^n + a_1 x^(n – 1) + . . . + a_n = 0 where a_0, a_1, . . . , a_n are integers. Let P = |a_0| + |a_1| + . . . + |a_n| + n...

I just wanted to check something. If I have a complex number of the form a = C * \exp(i \phi) where C is some non-complex scalar constant. Then the phase of this complex number is simply \phi. Is that correct?

The problem H(e^{j0.2\pi}) = {\frac{1 - 1.25e^{-j0.2\pi}}{1 - 0.8e^{-j0.2\pi}}} Solves to H(e^{j0.2\pi}) = 1.25e^{j0.210\pi} Attempts I'm really not sure how to get that answer, but I've tried a number of different approaches Multiplying by complex conjugate Multiplying by...

I am writing this in C#. Here is the code. using System; namespace ConsoleApplication3 { class Program { static void Main(string[] args) { int sum = 0; int uservalue; Int32.TryParse(Console.ReadLine(),out uservalue)...

Dear All, Hi! I am about to begin a Diploma in Aeronautical Engineering and would like to know if anyone could help me understand if in my future career of being an Aeronautical Engineer I would at any time be required to use Complex numbers to solve problems. If yes can you suggest examples...

I'm having trouble solving the equation m2 - n2 = 707, where n and m are natural numbers. Because there are 2 variables, even though they are discrete, the obvious thing to do would be to use another equation to solve for one of the variables and then insert the new form to the original...

Hello, please I need help. I have no idea how to start this. Can someone guide me? This is not homework, I'm just studying on my own and I really don't know how to begin this.

So i was messing around with egyptian fractions and i eventually decided to try adding them together and then reducing the one single fraction that formed into its lowest terms. Anyway i set them up with having 1 in the numerator ALWAYS (or else it won't work) and proceeded to add them up...

Let's say we have a result with the number 2624,499 and want to round it off to a certain number of significant figures. Some examples with different number of significant figures: a) 3 significant figures: 2420 or 2430? b) 4 significant figures: 2624 or 2625? c) 5 significant figures...

Homework Statement 8i = ( 2x + i ) (2y + i ) + 1 The final answers is [x =0, 4] [y=4, 0] Homework Equations The Attempt at a Solution The final answer in the book is stated as above but if I follow the solution I will get the real parts which would...

Can I get the link to the prime number theorem?

Find all values of $x$ such that $f(x)=x^2-19x+99$ is a perfect square for all $x\in N$.

Does anyone know of a reference work that lists natural numbers with unique properties? Like 26, for example, being the only natural number sandwiched between a square (25) and a cube (27). Does such a reference book exist? IH

I've been learning about polygonal numbers, and one of the exercises in this book ask me to show that 9t_{n}+1 [Fermat], 25t_{n}+3, and 49t_{n}+6 [both from Euler] are triangular numbers. I don't know how to approach these proofs, I've tried to show that they have some form similar to...

This problem is from Boas Mathermatical Methods 3ed. Section 16, problem 1. Show that if the line through the origin and the point z is rotated 90° about the origin, it becomes the line through the origin and the point iz. Use this idea in the following problem: Let z = ae^iωt be the...

I am reading a book about the interaction between atom and photon. I don't understand the following statement: "for the sake of simplicity, we assume the atom to be infinitely heavy and disregard the external quantum numbers" Q: what is the external (or internal) quantum number of an atom.

Physics Lab -- greatest common factor between all these numbers Homework Statement Hey, how can I find the greatest common factor between all these numbers? Please reply as soon as possible, it is an assignment due tomorrow. 27.69 3.15 0.59 4.71 18.08 22.84 31.08 19.11 21.91 9.7 38.78 42.82...

Are the less than (<) and greater than(>) relations applicable among complex numbers? By complex numbers I don't mean their modulus, I mean just the raw complex numbers.

If counting/positive numbers exist, do they imply the existence of negative numbers? I'd say yes, because there's always a bijection that maps the lowest counting number of the set to the highest, then the second lowest to the second highest, etc. This reversal of order/mirroring is possible...

Homework Statement Prove that if one chooses more than n numbers from the set {1,2,3, . . . ,2n}, then one number is a multiple of another. Can this be avoided with exactly n numbers? The Attempt at a Solution If we pick the top half of the set n+1 up to 2n we will have n numbers that are...

If a is a complex number, and a^2-a+1=0, then a^2011=? I tried using De Moivre's theorem, Taking a=cosθ+isinθ, but didn't get anywhere, got stuck at cos2θ+isin2θ-cosθ-isinθ+1=0. What do I do?

show that in a set of any 5 consecutive numbers there is at least one number that is co-prime to all the rest 4 (for example (2,3,4,5,6- 5 is co-prime to 2,3,4,6)

Guys, please help me figure this out: 1) how to calculate the largest prime less than 300 2) why 35 and 37 are not twin primes? 3) the smallest number divisible by five different primes Any input would be greatly appreciated)

I'm not sure whether this should go in this forum or another. feel free to move it if needed Homework Statement Suppose that z_0 \in \mathbb{C}. A polynomial P(z) is said to be dvisible by z-z_0 if there is another polynomial Q(z) such that P(z)=(z-z_0)Q(z). Show that for...

Hi everyone, I have studied QFT, the SM and the Higgs mechanism when I was in university and after reading an article from CMS (CERN) about the spin-parity measurement of the HZZ channel, which shows that J^{P}=0^+ is favoured versus J^{P}=0^-, I went back to the theory of the Higgs boson...

Is the set of the natural Nos complete?

Here is the question: I have posted a link there to this question so the OP can view my work.

Homework Statement Why isn't (3, -2 , 0 , 1/2) a valid quantum number? Homework Equations The Attempt at a Solution n=3 so l = -2 is valid. -l≤Ml≤l 2≤Ml≤-2 nonsensical statement. I don't know what to do...

Problem: All 4 digit numbers of the form $x_1x_2x_3x_4$ are formed by using digits $1,2,3,4,5,6,7,8,9$ such that $x_1\leq x_2 \leq x_3 \leq x_4$. a)Find the total number of such possible 4-digit numbers. b)The numbers are written in ascending order. If the number with rank 460 is abcd, then...

Hello, Homework Statement The complex numbers z_{1} = \frac{a}{1 + i} and z_{2} = \frac{b}{1+2i} where a and b are real, are such that z_{1} + z_{2} = 1. Find a and b. Homework Equations The Attempt at a Solution This looked like a time for partial fractions to me, so I went...

Problem: Let $\dfrac{1}{a_1-2i},\dfrac{1}{a_2-2i},\dfrac{1}{a_3-2i},\dfrac{1}{a_4-2i},\dfrac{1}{a_5-2i}, \dfrac{1}{a_6-2i},\dfrac{1}{a_7-2i},\dfrac{1}{a_8-2i}$ be the vertices of regular octagon. Find the area of octagon (where $a_j \in R$ for $j=1,2,3,4,5,6,7,8$ and $i=\sqrt{-1}$). Attempt...

Homework Statement I have to find the Thevinin Equivalent for the following circuit. I am assuming the current is going out of the node. V= node between inductor and capacitor V0 = V[40/(40-150j)] (V-75)/(600+150j) + (-0.02V0) + V/(40-150j) = 0 The only problem I have is with the last...

Homework Statement Suppose that u and v are real numbers for which u + iv has modulus 3. Express the imaginary part of (u + iv)^−3 in terms of a polynomial in v.Homework Equations The Attempt at a Solution |u+iv|=3 then sort(u^2+i^2) = 3 then u = 3 and v=0 or u=0 and v=3(0+3i)^-3 i swear i am...