Integer Definition and 606 Threads

Hi guys, Not actually a mathematics question as such (sorry) but does anyone know where i can get my hands on a copy of Chen's paper "On the representation of a large even integer as the sum of a prime and the product of at most two primes". For the life of me all i can find is references to it...

I need to multiply 2 matrix in Mathematica but modulus an Integer. The "Modulus->n" option cannot be used with "Dot" function. You can use Modulus-> n with "Inverse" or even "Det" but not with "Dot". It is something strange. How should I do it, then? Any idea? Thank you.

Homework Statement The product of N 4-digit consecutive integers is divisible by 2010^2. What is the smallest N value? Multiple choice answers range from 4 to 12. Homework Equations N/A The Attempt at a Solution I tried multiplying the smallest combo possible 1000x1001x1002x1003...

I need to show that \sum_{i=0}^n i^k=\Theta(n^{k+1}) Or equivalently \lim_{n\to\infty}\frac{\sum_{i=0}^n i^k}{n^{k+1}}=CI simply don't know what to do with the sum here. I know that I can rewrite or expand it, but that doesn't seem to help me. Any suggestions? Thank you!

Greatest Integer Function.. help! Homework Statement Well this is the problem a plomer charges 80 bucks ones he arrives at your home and charges and extra 25 per hour.. Give the equation,, Kind of i don't get it is for extra credit but still i don't like it when i don't know how to do it...

Lets asume that electron is in state: \left[ \begin{array}{c} \psi(\vec{r})\\ \phi(\vec{r}) \end{array} \right] It's a vector because electron has two spin components (up and down). If we rotate our labolatory by the angle 360^0 we got: \left[ \begin{array}{c}...

Let J be total angular momentum, L - orbital angular momentum and S - intristic momentum (spin). Squares of these operators have appropriate eigenvalues j(j+1), l(l+1), s(s+1). Which of these numbers j,l,s should be integer. I know that spin can have half-integer values. But probably orbital or...

Hi I'm playing around with partitions and have come up with an integer sequence representing the maximum number of partitions of various "widths" that display the following properties: - min values in partition are equal - max values in partition are equal - partitions contain equal number of...

Proof: N2 > N rules out all the others. :-p

This is the equation given for the Y. Y_{p}=\frac{J_{p}(x)cos(p\pi)-P_{-p}(x)}{sin(p\pi)} In many books, if p is an integer n, they just said Y_{n}=lim(p\rightarrow n) Y_{p} J_{p}(x)=\sum^{k=0}_{\infty}\frac{(-1)^{k}}{k!\Gamma(k+p+1)}(\frac{x}{2})^{2k+p} which give...

In several places I have come across what seems to be a standard proof by contradiction that there is no greatest natural number. As follows:- Assume there is a greatest natural number (+ve integer). Call it n. Add 1 to it to get n+1. n+1 is an integer greater than n. Therefore n cannot be...

Homework Statement Prove: If a and b are in N the [(1,1+a)] + [(1,1+b)] = [(1,1+a+b)] Homework Equations Definition: We define + over Z as follows: if [(a,b)] and [(c,d)] are any two equivalence classes, we define [(a,b)] + [(c,d)] = [(a+c,b+d)]. The Attempt at a Solution So...

why not half-integer? according to the definition, such as [J_z,T^k_q]=q T^k_q it is quite possible that k can be a half-integer.

my midterm is in 4 hours and this actually the only thing i need help with. Homework Statement prove using squeeze theorem that lim(x-> +inf) (x^2 - [[x^2]])/x = 0 Homework Equations g(x)<=f(x)<=h(x) [squeeze theorem] The Attempt at a Solution on the assignment i didn't know we...

Homework Statement Show with mathematical induction that \frac{n^5}{5} + \frac{n^4}{2} + \frac{n^3}{3} - \frac{n}{30} \in {Z} for all n\ge 1. Homework Equations Probably. The Attempt at a Solution Inductive statement: Q(n): \frac{n^5}{5} + \frac{n^4}{2} + \frac{n^3}{3} -...

Homework Statement A cube of sides a*a*a is in 3 dimensional space. All eight of its corners have integer coordinates. Prove that a is an integer. Homework Equations - The Attempt at a Solution First, I considered three corners of the cube p, q and r, with these, two vectors...

I was wondering if anyone could give me some hints on this Suppose A^k=0 for some integer k is greater than or equal to 1. Prove that A is not invertible.

I'm studying for a test. In doing one of the old tests and it had a question that I couldn't do. Let T: Rn \rightarrow Rn be an operator on Rn, where n is an odd positive integer. How do I prove T has at least one eigenvector in Rn

Prove or disprove: sinh2(ln(\sqrt{}2+\sqrt{}3)) is an integerObviously, I used my calc to figure out that the answer is 2. Proving it w/o a calc is hard though. The Attempt at a Solution I've tried rewriting sinh2 as (1/4)(e2x+e-2x-2) and after all the substitutions and log rules I get...

positive operator proof Homework Statement Prove that if T ∈ L(V) is positive, then so is Tk for every positive integer k. Homework Equations The Attempt at a Solution Let v=b1v1+...+bnvn. Now since T is positive, T has a positive square root. T=S^2. <S^2v, v>=<S^2v1...

I've been stuck on this for a while now, and I was wondering if anyone could help me out. The problem is: If ax^{2}+bx+c=0, prove that all integer roots divide b I'm fairly new to number theory, but this is the one problem that's been really tough for me. If someone could even give me...

This may be a stupid question or have a pretty obvious answer, but I can't seem to find one so I'll just go ahead and post :) I was looking at some empirical data for relationships defining (abstracted) values for ionization and recomination coefficients in gases as a function of electric...

First Question: Let Nn be the integer whose decimal expansion consists of n consecutive ones. For example, N2=11 and N7=1,111,111. Show that Nn|Nm iff n|m. Second Question: If (a,c)=1, prove that (a,bc)=(a,b). On the second question I can see that it is true because a and c are...

This problem comes from Sheldon Ross's book "A First Course in Probability (6th ed)." There are 5 hotels in a certain town. If 3 people check into hotels in a day, what is the probability that they each check into a different hotel? Attempt at a solution: There are 5C3 = 10 different...

Homework Statement Let R be a ring and suppose there exists a positive even integer n such that x^n = x for every x in R. Show that -x = x for every x in R. Homework Equations The Attempt at a Solution I solved the case where n = 2. Let x be in R. (x+x)^2= x+x = 2x...

This was a problem on a final test I took this april in Reykjavík University and I whould be greatful if you could help me with it. Homework Statement Let f(x,y)=2x*cos(y^4) be a function and let D be area in R^2 defined by 0≤x≤1 and x^(2/3)≤y≤1. Calculate the double integer: ∫∫f(x,y)dA...

Homework Statement In spherical polars, the azimuthal part of the wavefunction of a particle is psi(phi) = 1/sqrt[2.pi] . exp[i.m.phi] where phi is the azimuthal angle. Show m must be an integer.Homework Equations I know you are supposed to have a good go at solving the problem first, but...

This is causing me a bigger headache than I anticipated. Basically, given an integer N and a number M, I need a list of all the possible integer partitions of N into M parts such that each part is strictly positive and each part is UNIQUE. I don't want repetitions. Just unique ones. So for...

Hi everyone, I'm trying to assign a string in combination with an integer to a variable v. The string-part is fix, the integers comes from another variable n. For Example: n:=10; Print("Sym_",n); The output of "Print(...);" (that is "Sym_10") should be assigned to another variable...

Hi, I have no idea on how to start to do this question. If the square of an integer is even,then the integer itself is even I try to check some books but i can't get any similar examples.I wonder if I can directly prove the n=2k, n^2 = 2(2k^2). Thanks!

How would I find values for A and B such that AB-A-B=1673 Where A and B are integers? I know the answer (28 and 63), but I want to know how to arrive at that answer without any guessing, or at least with a minimum amount of guessing. Are there any other solutions? I just made this...

Let x and y be n-tuples of non-negative integers. Furthermore, sum x_i = sum y_i and, sum x_i^2 = sum y_i^2 Is it true that x must be a permutation of y? Cheers!

N is a seven digit base-8 positive integer having the form ABCDEFG that uses each of the nonzero base-8 digits 1 to 7 exactly once, and satisfies these conditions: (i) ABCDEFG is divisible by 7. (ii) ABCDEF is divisible by 6. (iii) ABCDE divisible by 5. (iv) ABCD is divisible by 4. (v)...

Can someone help me on how exactly to do this? I'm trying to read an integer string and each "digit" in the string is put at the front of the linked list (i.e. reverse order). When I print it out I want it to reverse again. I know I'm not implementing it right because when I run it the program...

Hello, Can an integer always be represented through the multiplication of two or more integers? (Are all integers divisible by some set of 2 or more integers (- or +)?) For example, 8 is can be represented by 1 x 8, 2 x 4 and 2 x 2 x 2. But what about 257 or even - integers? I'm trying...

The other day I was thinking about the integer power sum and the general solution for each value of p. I came up with a method that will allow me to calculate the general solution. I thought that I may have stumbled upon something novel, because I couldn't find any reference to this method...

Well, the problem statement is in the title: Given that n is an integer, show that 3n2 - 1 can't be the square of an integer. Currently, I don't have any idea at all where to start. Method is probably to assume opposite and show that this leads to a contradiction. Any hint as to where to...

Homework Statement if z = 1/sqrt 2 + i/sqrt2 Homework Equations show that z + z4n+1 = 0, when n is any odd integer. if n is an even integer, find z + z4n+1 in rectangular form. The Attempt at a Solution I have no clue where to start...

the integer part is ... (?? distributive ??) Homework Statement Define the floor of a real number k where [k] is the least smallest integer from k. I want to show that [a - b] = [a] - [b] Homework Equations n/a The Attempt at a Solution [1.2 - 5.7] = [-3.8] = -4 [1.2] - [5.7]...

Homework Statement switch statements. y is an integer number. Use a switch statement to set B equal to one of the following values: true, false, or the vector [1 0 1]. If y is {1,2,3,5,7}, then set B to true. If y is {4, 6, 8, 10}, then set B to false. If y is neither, then set B to the...

Homework Statement A is an invertible integer matrix. Prove that if det A = 1 or det A = -1, then the inverse of A is also an integer matrix. Also prove the reverse, if A-inverse is an integer matrix then its determinant is 1 or -1. Homework Equations I'm not too sure how to start...

Why 30 is the largest integer such that none of its...? Why 30 is the largest integer such that none of its totatives are composite? which means All the coprime numbers that below 30 are primes.. 30=> 7,11,13,17,19,23,29 ?// and if you have a proof that it is the biggest integer please Help...

Homework Statement Prove that 3 divides one of the integers n, n + 2, or n + 4, for any integer n. Homework Equations The Attempt at a Solution

Homework Statement Prove that the expression \frac{a(a^2 + a)}{3} is an integer for all integers \geq 1 Homework Equations The Attempt at a Solution a(a^2 + a ) = 3q + r r can be: r = 0,1,2 for r = 0 \frac{a(a^2 + a)}{3} = q q is an integer by the division algorithm. When I...

ABCDEFGF is an 8-digit positive decimal integer, where each letter represents a different decimal digit from 0 to 9. The digits 1 and 9 do not appear. The nonzero even digits appear in ascending order, and the odd digits appear in descending order in ABCDEFGF. None of A and E can be zero...

Determine a 9-digit positive integer that uses each of the decimal digits from 1 to 9 exactly once, such that: (i) The sum of the digits 1 and 2 and all the digits between them is 9. (ii) The sum of the digits 2 and 3 and all the digits between them is 20. (iii) The sum of the digits 3...

For integer x only, is x! considered a polynomial?

so I have to prove that a^3-2b^3-4c^3 = 0 has no positive integer solutions. I have gotten through most of the proof but now I am stuck, and if you guys could give me a nudge in the right direction that would be great. work done so far: proof by contradiction, i assumed that...

Homework Statement show that every positive integer can be written as the product of a square and a square-free integer (an integer that is not divisible by any perfect squares other than one The Attempt at a Solution well i can see by example that this works: i.e 60=22*3*5...

Homework Statement Find the largest positive integer n such that n^3 + 100 is divisible by n + 10. Homework Equations The Attempt at a Solution The hint I've been given is to use (mod n + 10) to get rid of the n. but i don't quite see how it would work :S all my attempts...