Integer Definition and 606 Threads

Show that if n is a positive integer, then C(n,0) < C(n,1) <...<C(n, floor(n/2)) = C Homework Statement Show that if n is a positive integer, then C(n,0) < C(n,1) <...<C(n, floor(n/2)) = C(n, ceiling(n/2)) > ... > C(n, n) Homework Equations none The Attempt at a Solution Seems pretty...

Homework Statement If a \in Z, then a^3 \equiv a (mod 3) . 2. The attempt at a solution Proof: Suppose a \in Z. Thus a is either odd or even. Case 1: Let a be even. Thus a = 2k, for some k \in Z. So a^3 - a = 8k^3 -2k = 2(4k^3 - k) = 2(k)(2k - 1)(2k + 1). Notice that, for all k...

I know that the fundamental theorem of arithmetic states that any integer greater than 1 can be written as an unique prime factorization. I was wondering if there is any concept of negative prime numbers, because any integer greater than 1 or less than -1 should be able to be written as n = p1...

Hi guys, i am using the C language and have created the following function: void counter (double c) { FILE *fp; char output[]="output.xls"; int n,p=0; int r=0; int i,j; float x=0; fp=fopen(output,"w"); fprintf(fp,"rmax\tnumber of particles within rmax\r\r\n"); for(n=1;n<=10;n++)...

Hello all, Is there a closed form expression for the convergence of C(s) = \sum_{n=1}^{N} n^{s} Cheers, Adrian

Number theory: confused about the phrase "an integer of the form" Homework Statement Prove that any prime of the form 3k+1 is of the form 6k+1 Homework Equations The Attempt at a Solution I'm not sure where to start at all. I tried rewriting 3k+1 as 6k+2=6k+(6-4)=6(k+1)-4. But...

Hello everyone! I am trying to construct an algorithm for the following problem and was wondering if there is any existing body of knowledge on this. Please forgive me if this is inappropriate (or ridiculous) but I am totally foreign to number theory. It goes like this: You are given n...

Beaconaut APICalc 2 just released on Jan.18, 2011, which is an arbitrary-precision integer calculator for bignum arithmetic, cryptography analysis and number theory research... http://www.beaconaut.com/forums/default.aspx?g=posts&t=13"

Homework Statement For what integer value of X is 3x+5> 11 and x-3 <1?

Hello everyone Thanks for viewing this topic for me... my question is when I tried to check user inputs a valid age it works only if a number is entered. If by mistake user inputs a character value (e.g. any character a to z or any symbol) this loop runs infinite How can I check if a...

Homework Statement I can't find a step by step explanation for solving these types of equations eg. 99 = [2x+1]/3 Homework Equations eg. 99 = [2x+1]/3 or 48 = 4[2x/3] How do you handle the multipliers iand constants inside the brackets? thx [b]3. The Attempt at a...

Homework Statement This is just a problem i came up with while doing in equations, and recently saw in a book too. Find the smallest integer n, for which n! > 10n The Attempt at a Solution The trial method (with help from the computer) yields 25 to be the answer. After a...

How to solve that eqation? 3^x=4y+5

Hi everybody! I'm studying the IQHE and I want to understand the rise of the diophantine equation. I read the thouless article but it was no so conclusive. I've also read the kohmoto article (phys rev B 1989) and he says that that property comes from the darboux theorem but i don't...

Homework Statement This is a proof problem in the mathematical induction section of my textbook. I am having trouble with question (c). Result: 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6 for every positive integer n. (a) Use the result to determine the formula for 22 + 42 + 62 + ... + (2n)2 for...

Homework Statement Suppose that n is an odd integer. Prove that n is either one greater than a multiple of 4 or one less than a multiple of 4. Homework Equations N/A The Attempt at a Solution I realize that this is going to be a direct proof. However, I am stumped on where to...

Homework Statement For some integer n, a|(4n+3) and a|(2n+1). Therefore, 4n+3 is an integer multiple of a, as well as (2n+1). Prove or disprove that a=+/-1. Homework Equations N/A The Attempt at a Solution I have been working on this one for quite some time now, but I cannot...

Homework Statement Calculate the integer part ( whole number part ) of 1 + 1/sqrt ( 2 ) + 1 / sqrt ( 3 ) + 1 / sqrt ( 4 ) + 1 / sqrt ( 5 ) + ... + 1 / sqrt ( 1 000 000 ) Any hints? Thanks, I'd appreciate the help

Homework Statement let a,b be positive integer , c is real number, and -a<c<b i want to show there exist integer m, -a \leq m \leq b such that m-1 \leq c<m i don't know any easy method, but this is where i got now, Let set S=[m|-a \leq m \leq b] So by contradiction, suppose that for all m...

When looking for potential factors of an integer, I noticed that I could predict the frequency of the greatest integer function quotient and use this prediction to jump to the next potential factor. See the attachment for an example. I don't know if someone else had already discovered this...

Homework Statement Let k be any positive integer. Prove that there exists a positive integer multiple n of k such that the only digits in n are 0s and 1s. (Use the pigeonhole principle.) Homework Equations The General Pigeonhole Principle If more than mk things are distributed into k...

Hey there, physics forums! A question occurred to me the other day: Is it true that if f \in \mathbb{Z}[x] is monic and irreducible over \mathbb{Q} , then for at least one a \in \mathbb{Z} , f(a) is prime? I can't prove it, but I suspect it's true. Does anyone know if this problem...

Homework Statement √(3+2√(2)) can be simplified into a fairly simple sum of two number: one is an integer and one is an irrational number . Find them and show you are correct by squaring both sides of the "equation" Homework Equations The Attempt at a Solution

Hello PhysicsForums! I was reading up on UFD's and I came up with a few quick questions. 1. Why don't the integers of Q[\sqrt{-5}] form a UFD? I was trying to tie in the quadratic integers that divide 6 to help me understand this, but I am stuck. 2. Why is Z a UFD? 3. Assuming Q[\sqrt{d}] is...

Homework Statement I want to prove that a polynomial f(x) and a polynomial g(x) with degrees of k,n where k,n are positive even integer, n>k that limit x-> - infinity of f(x)-g(x)=-infinity Homework Equations a polynomial can be written as a1x^n+a2x^(n-1)...+a(n-1)x+an The...

[bHomework Equations none The Attempt at a SolutionHomework Statement Homework Equations The Attempt at a Solution

Homework Statement Prove that either [a]_{n}\cap[b]_{n}=empty set or [a]_{n}=[b]_{n}.Homework Equations The Attempt at a Solution I want to assume there is an element x in [a]_{n}\cap[b]_{n} and show this implies [a]_{n}=[b]_{n}. This tells me x is in [a]_{n} and [b]_{n}. That's where I get stuck.

I have 2 questions here. I know there is a lot of text, but don;t be scared or deterred from helping please, it is simple to understand and mostly just text/explanation. The Second one is very long, the first not so much. 1)Problem: Complete the proof of Observation 4.2 by showing that every...

Homework Statement find p,q,r,s integer solution \frac{1}{p^2}+\frac{1}{q^2}+\frac{1}{r^2}+\frac{1}{s^2}=1 Homework Equations here some alternate form you can see http://www.wolframalpha.com/input/?i=1/p^2%2B1/q^2%2B1/r^2%2B1/s^2%3D1 The Attempt at a Solution i don't know...

Homework Statement let x,y \in N. Solve the equation \frac{1}{x}+\frac{1}{y}=1 Homework Equations n/a The Attempt at a Solution so i can see x=y=2 is the solution, hmm, isn't there any other solution. and, this is one of three of my assignment question for 15% continuous...

Homework Statement prove that if a and b are both odd integer, then 16|(a^2+b^2-2) Homework Equations n/a The Attempt at a Solution let a=2m+1 \ and \ b=2n+1, then a^2+b^2-2=4(m(m+1)+n(n+1)) so its divisible by 4, and also divisible 8 since m(m+1) \ and \ n(n+1) are even. so i only prove...

In the situation where differences between consecutive squares, (or consecutive cubes, consecutive x^4, etc.) are calculated, then the differences between those differences are calculated, and then the differences of those differences, and so on until you reach a constant number at a deep...

Find all integers n for which the fraction n ^ 3 + 2010 / (n ^ 2 + 2010) is equal to integer. please I need help :( Thank you

Hi all, I am new to topology & geometry. I skimmed through the subject in various books so I might be asking simple questions. My question is how can we say Chern's class belong to Integer rather than Real cohomology class? I assume one defines it through the characteristic polynomial of...

Homework Statement n2 has the form 3k or 3k+1 for some integer k Homework Equations n/a The Attempt at a Solution i've tried to table it for me to see, but still i don't have the general idea, should i show n2 is either divisable by 3k or 3k+1? if yes i still don't know owho

Please help - I am helping a student who is trying to translate Ong-Schnorr to C++ or VB.net language. My major was electronics so I am not sure how to interpret inverse random integer k. Any one ? or suggest me a reference to read on - much thanks, newbie Ong-Schnorr-Shamir (from Briuce's...

A problem asks to find all possible pairs (x, y) of positive integers that satisfy the equation: x3 = y2 – 15 There are 2 pairs (so far) that satisfy the equation: x = 1, y = 4 x = 109, y = 1138 It's possible that these 2 points are the only two positive integer solutions...

I am struggling to understand the proof for integer parts of real numbers. I have used to mean less than or equal to because I could not work out how to type it in. I need to show that: ∃ unique n ∈ Z s.t. nx<n+1 The proof given is the following: Let A={k∈Z : kx} This is a...

I am attempting to program Mathematica to multiply the square free terms of an integer. Basically say we are looking at 252, its prime factors are 2^2*3^2*7. So what I want to do is have Mathematica return to me just 2*3*7 when I enter 252. So I have this S := FactorInteger[252]...

i am a student of physics i do not know much about the chern number i wonder why the chern number must be an integer any good reference?

The requirement is to find an pseudorandom integer sequence i0, i1, i2, i3, ... , i48, i49 so that there are at least 15 adjacent differences which are greater than 36. Adjacent difference = absolute value of the difference between two adjacent integers = |i - i | where j = 0 to 49 | j -...

Find smallest d=2a^2=3b^3+2=5c^5+3 where a,b,c are integers. This problem is very hard. Either no solution or d is toooooooo big

I know that \sin^2 b= (\sin b)^2 and in general \sin^n b=(\sin b)^n if n is a positive integer . What if n is a negative integer , would it be \sin^{-1}b=(\sin b)^{-1}=\frac{1}{\sin b} I don't think this is right , because properties of indices only works for numbers and NOT function...

Homework Statement I need to prove that a composite integer n>1 has a prime divisor p with p<=sqrt(n). Homework Equations The Attempt at a Solution Im not sure how to do this, any help getting started would be great thanks.

Homework Statement For each positive integer n, let T(n) be the number of triangles with integer side lengths, positive area, and perimeter n. For example, T(6) = 1 since the only such triangle with a perimeter of 6 has side lengths 2, 2 and 2. (a) Determine the values of T(10), T(11) and...

Homework Statement Disprove or prove the statement that every positive integer is the sum of at most two squares and a cube of non-negative integers.2. The attempt at a solution I'll call the numbers that can be squares a and b. C will be the cube. The easiest way to disprove something is to...

Take two rows of respective length m and n: a1, a2, a3,..., am and b1, b2, b3, ..., bn. Then produce as follows the generated array Gai to contain these elements: a1, a1+a2, a1+a2+a3, ..., a1+..+am, a1+..+am+a1, a1+..+am+a1+a2, ... Alike produce the generated array Gbj to contain...

Homework Statement Prove that every integer n>= 14 is a sum of 3's and/ or 8's. Homework Equations Induction Hypothesis The Attempt at a Solution Base Case: P(0): Suppose n= 14, and k is an integer representing number of times 3 or 8 is added: 14= 3k; k=14/3 ( this shows...

Hi Everyone, I am reading up on information theory, and every resource I have found on the topic which derives the form of entropy uses the following inequality as part of the proof. Let n be a fixed positive integer greater than 1. If r is an arbitrary positive integer, then the number...

Square of integer is quite easy, childlike stuff. But there is no harm in seeing a known thing in different lights. Experimenting on any thing is always fun, at least initially. So, while reading some stuff on semiconductor physics I came to think about viewing square of integer in different...