Integers Definition and 467 Threads

counterexample so that (ab)^i=a^ib^i for two consecutive integers for any a and b in a group G does not imply that G is abelian. this is a problem in herstein and I'm struggling to find an example. The previous problem to show that if (ab)^i=a^ib^i for 3 consecutive integers then G is...

Given 3 equations: 1) 1/2pi + 2Pi(x) = 3.90625F 2) pi + 2Pi(y) = 7.65625F 3) 3/2pi + 2Pi(z) = 11.2500F Find such F so that x, y and z are integers; maximum error on the left side can be +- pi/7. How would you tackle this one? I am still trial'n'erroring..

Homework Statement http://math.stanford.edu/~vakil/putnam07/07putnam2.pdf I am working on problem 5. It is clear that the integers will not change if they can be totally ordered by divisibility, but I need help proving that they will reach such a state. Obviously after every step, the...

Homework Statement If m is an odd integer and n divides m, then n is an odd integer. Homework Equations Odd integers can be written in the form m=2k+1. Since n divides m, there exists an integer p such that m=np The Attempt at a Solution We will assume that m is an odd integer and...

Someone please help me with this qiestion: Prove that for all integers a, b, and c, if a divides b but not c then a does not divide b + c, but the converse is false. Thanks.

I want to use arbitrarily long integers in Csharp, can you tell me how to declare and use this. Please explain the namespace, classes used as I'm very new to this. Thanks.

We know that the function f(x) = sin(2*pi*x) vanishes at all integers, are there other functions like that and what is the appropriate generalization to higher dimensions? Cheers

How can I prove this? Suppose X is a set of 16 distinct positive integers, X=\left\{{x_{1}, \cdots , x_{16}}\right\}. Then, for every X, there exists some integer k\in\left\{{1, \cdots , 8}\right\} and disjoint subsets A,B\subset X A=\left\{a_{1},\cdots\ ,a_{k}\right\} and...

Help! Please I am trying to write a Lisp program to calculate the sum of the first N positive integers where, for example, when N = 6 the sum of the first N = 21 Any Ideas?

I already know that this is true for galois extensions of Q... how do you extend this result to any finite extension of Q? I was thinking given a finite extension of Q, call it K... find a galois extension that includes the finite extension, call it L... then somehow use the fact that the...

I just took a number theory midterm, the professor had a question the that said "Show by induction that for all integers n, 4^{n} is congruent to 1 +3n mod(9). Now am I crazy or did the professor probably mean to say integers greater or equal to 0, or for any natural number n, ...

Why does does the following code not compile? PROGRAM TYPES INTEGER A(3) A(1)=1 A(2)=2 A(3)=3 CALL SUBR(A) print *,'Done' RETURN END C --- Here is a subroutine ----- SUBROUTINE SUBR(A)...

It is well known that 4n(n+1) + 1 is a square if n is an integer but if n is a Gaussian integer i.e., 4n(n+1) + 1 = A + Bi, then the norm (A^2 + B^2) is always a square! The proof is quite easy since A = u^2 - v^2 and B = 2uv.

Hi! i have a problem about swapping three integers in C program. Usually i use the call by reference for two integers only. Now for three i can't get t.

The mathematical symbol for real numbers is R, with another vertical line coming down on the left side of the R. What is the mathematical symbol for integers? can anyone draw it?

Does anyone do these? Sudoku is based on magic squares, Kakuro is based on partitions of integers. I haven't really tried solving any yet but my first impression was that Kakuro is generally tougher than Sudoku (for me anyway). http://en.wikipedia.org/wiki/Kakuro

Let n be a positive integer. Define a sequence by setting a_1 = n and, for each k > 1, letting a_k be the unique integer in the range [tex]0 \le a_k \le k-1[/itex] for which \displaystyle a_1 + a_2 + \cdots + a_k is divisible by k. For instance, when n = 9 the obtained sequence is \displaystyle...

Okay, I know that this is probably super easy. This is not homework, I just grabbed tis book at the library today and am trying to get familiar with the subject (Abstract Algebra). The book is hella old and doesn't have many of the solutions, especially if the author regarded the solution as...

Hello all. I reluctantly ask this question because it is probably,as the text states easy, but my desire to clear this point up overides my fear of looking a fool. I quote word for word but will use words instead of the belongs to symbol. A subset S of the set Z of integers is a...

Homework Statement I need to find the congruence classes mod (3 + sqrt(-3))/2 in Q[sqrt(-3)]. Homework Equations None known. The Attempt at a Solution I'm not sure how to go about finding these congruence classes. I know that in the regular integers congruences classes mod x are...

Homework Statement For my number theory course, I'm supposed to come up with a definition of congruence in quadratic integers, and define the operations of addition, subtraction, and multiplication. Homework Equations None known. The Attempt at a Solution I honestly have no real...

Hi, just can't get my head around how to draw these three graphs. Any help appreciated. Thanks In each case below, draw the graph of a function f that satisfies the given property. Give an example of a function f : N -> Z that is bijective/that is injective but not surjective/that is...

Are integers such as n=1,2,3 etc in Bohr's atomic theory, exactly whole numbers or just very close to being whole numbers?

Hi! I was thinking about primes and have a bit of a question. I apologize if this is too easy or obvious -- I haven't thought much about it. Take two relatively prime numbers, P and Q. P < Q, and P is not prime. How many pairs (P,Q) are there so that ALL positive integers which are...

I am fairly certain that \frac{n}{p_n} is not monotone for any n, but I can't give a proof of it without assuming something at least as strong as the twin prime conjecture. I was wondering if anyone has some advice to prove this using known methods?

Specify the steps of an algorithm that locates an element in a list of increasing integers by successively splitting the list into four sublists of equal (or as close to equal as possible) size, and restricting the search to the appropriate piece. (Hint: see binary search algorithm.) can...

hi I am having trouble with this question: Q:Express the number as a ratio of integers. 9.4(78)bar so 9.4787878787878787878 what is confusing me is the 9.4, and where i should start the series at 78/10^(?) please if someone could help me. ty

Wow, I'm totally lost on where to start for this one. In this chapter we have been working with r-combinations with repeition allowed and using the form of(r + n - 1) (r ) Where n stands for categories, so if you had 4 categories u would use 3 bars to break up the categories. And r...

how to convert an input of integer(more than 1 character) type into output which is in string in c++

Hello everyone. He told us he could of course change the parameters which he will of the proofs we have been working on so I'm testing out some cases but I want to make sure I'm doing it right. Here is an example of a proof the boook had...

Prove that for all integers n, n^2-n+3 is odd. stuck on algebra part :( The question in the book is the following bolded statement. Prove that for all integers n, n^2-n+3 is odd. I rewrote it as this, is that right? For all integers n, there exists an integer such that n^2-n+3 is odd...

I'm sure it exists, and it'd help me to have it. Thx!

Hello everyone. I'm wondering if I'm allowed to use a counter example to disprove this. I'm not sure if I'm understanding the statement correctly though. THe directions are: Determine whether the statement is true or false. Justify your answer with a rpoof or a counterexample. Here is...

We are currently using Dummit & Foote's Abstract Algebra book in a gradute course of the same name. Recently, I had an issue concerning the additive and multiplicative integer groups mod n, which I brought to the professor's attention. The issue deals specifically with the way these groups are...

This is probablly a silly question but it has been bothering me for a while. How can there be for example an infinite amountof integers? each integer has an integer that is smaller than it by one and an any number that is one bigger than a finate number is also finate. doesn't this prove that...

How I can write a program which reads a sequence of integers and counts how many there are. Print the count. For example, with input 55 25 1004 4 -6 55 0 55, the output should be 8 because there were eight numbers in the input stream. Please help.

Hi all, I'm doing a little programming at the moment using Dev-C++. I'm writing a windows program, and have all of the stuff like menus, dialog boxs etc sorted out, and now need to get onto the programming that makes the program achieve something. In the program I will be dealing with very large...

The sum of two intergers is twenty. Five times the smaller interger is two more than twice the larger integer. Find the integers. I'm somehow lost on the problem I tried setting the problem up to solve for the smaller varrible. Making it x & the larger 20-x. Anyway, I came up with 5x...

Hi, I'm curious if the following statement is true for all prime numbers n, \det_{\mathbb{Z}_n}M = (\det_{\mathbb{R}}M)\mod n where \det_F M is the determinant of M over the field F. Thanks. James

Let,s suppose we want to do this sum: 1+2^{m}+3^{m}+...+n^{m} n finite then we could use the property of the differences: \sum_{n=0}^{n}(y(k)-y(k-1))=y(n)-y(0) so for any function of the form f(x)=x^{m} m integer you need to solve: y(n)-y(n-1)=n^{m} i don,t know how to...

I'm really stuck on the following problem: I'm trying to determine whether or not 5^10^5^10^5 is divisible by 11... i have tried a few different methods and can't figure this out. I know the trick must have something to do with modulo 11, but I am not sure exactly how to get the...

hi everybody, I have a question in math to figure out the general term for the sum of the pth powers of n integers. I found a formula called faulhabers formula to do this question, but I do not understand the method behind it. can someone please help me?

Q.Prove that 1+1/2+1/3+1/4+...+1/n is not an integer.n>0

Could somebody explain with due brevity why/how the set of p-adic integers is homeomorphic to the Cantor set less one point for any prime p? This is a quote from Wikipedia:Cantor Set: "The Cantor set is also homeomorphic to the p-adic integers, and, if one point is removed from it, to the...

I was working with Fourier series and I found the following recursive formula for the zeta function: \frac{p \\ \pi^{2p}}{2p+1} + \sum_{k=1}^{p} \frac{(2p)! (-1)^k \pi^{2(p-k)}}{(2(p-k)+1)!} \zeta(2k) = 0 where [itex]\zeta(k)[/tex] is the Riemann zeta function and p is a positive integer. I...

While responding to another thread about summing nth powers of integers, I came up with what might be a new method. There is an old one (Faulhabers formula) http://mathworld.wolfram.com/FaulhabersFormula.html" , but mine seems to be considerably simpler. Most likely, someone has already...

Find the quotient field of a ring of Gaussian integers?

Prove that summation of n(n+1)/2 is true for all integers. Why is my proof not valid? Could someone explain to me how this is not a valid proof of the summation of "i" from i=1 to n: n(n+1)/2 Show for base cases: n=1: 1(1+1)/2=1 n=2: 2(2+1)/2=3 n=3: 3(3+1)/2=6 ... inductive...

I have a found a hypothesis which I would like you to look at, and perhabs (dis)prove.. ----------------- All integers (n) bigger than 2 (3, 4, 5, 6, ...) be descriped as: n = (p_1 * p_2 * ...) + k where all p and k are primes, but also include 1. Notice that k < (p_1 * p_2 * ...), and...

a = 238000 = 2^4 x 5^3 x 7 x 17 and b = 299880 = 2^3 x 3^2 x 5 x 7^2 x 17 is there an integer n so that a divides b^n if so what is the smallest possibility for n