Integer Definition and 606 Threads

I am coming across hiccups in my proof process. I am given this problem - Prove: if n is an integer and 3n + 2 is even that n is also even. I have to apply a contrapositive proof to this problem. The form is then \negq therefore \negp .The problem becomes - if n is odd, prove that 3n+2 is even...

Homework Statement m and n are positive integers with m,n≥2 where m^2=kn^2 The Attempt at a Solution we know that all prime factors of m have an even amount , their are no prime factors that are repeated an odd number of times. The same goes for n. if k is not a perfect square...

The logic that odd composite with least difference will be factored easily and large difference would factored hardly is wrong. B'coz whatever be the difference between the factors their exist Best Fermat Factors to make the Fermat factorization easier. Please follow the link to know more...

Homework Statement I'm making a program which will convert mph to minutes and seconds per mile. For example my program will take 6.5 mph and convert it to 9 minutes and 13.8 seconds per mile. But being new to programming I don't know how to convert a double value to an int value (I believe its...

Homework Statement Let m be a positive integer that has an odd divisor greater than 1. Prove (by contradiction) that \log_2{m} is not an integer. Homework Equations The Attempt at a Solution I'm not sure where to begin here. The book I'm working with provides a similar example, but it...

Homework Statement k(x)=x2*[1/x] for 0<x≤1 k(x)=0 for x=0 Find where k(x) is differentiable and find the derivative Homework Equations The Attempt at a Solution I know that it is differentiable for all ℝ\Z on (0,1], but I am unsure how to find the derivative for this problem.

Homework Statement Let p be a prime and let n≥2 be an integer. Prove that p1/n is irrational. Homework Equations We know that for integers a>1 and b such that gcd(a,b)=1, a does not divide b^n for any n≥ 1. The Attempt at a Solution To prove irrationality, assume p^(1/n)=a/b for...

Homework Statement On a 8x8 chess board format an Integer program to optimize the amount of knights required such that every square is covered by at least one knight. Homework Equations I know of a similar problem where we use duality for the placing 5 queens such that the maximum...

Homework Statement Prove that the limit exists. lim 5 - 1/2[[2x]] x-->1 Show your solution.. Homework Equations The Attempt at a Solution Tried getting the limit from the right and left.. not sure if what I've done is right though but this is what I got. lim 5 -...

Homework Statement I know you could prove this by stating every integer is either 3m, 3m+1 or 3m+2. However I am trying to prove this just using either even numbers or odd numbers. so for example, when I try: (2x+1)^2 = 4x^2 + 4x + 1 - expand = 3x^2 + x^2 + 3x + x + 1 - group like...

Ok so I was trying something in C when i found something i don't understand:- code is:- int c = 1; printf("%c\n",c); (not writing the include and return 0 stuff) so when i run this it gives an output of a 2x2 box like this:- 0 0 0 1 whats happening. When i put the 1 in commas like this int c=...

Find no. of Integer value of $\left(a,b\right)$ which satisfy $4^a+4a^2+4 = b^2$

Question: Show that the derivative of f(x) = (x-a)m (x-b)n vanishes at some point between a and b if m and n are positive integers. My attempt: f(x) = (x-a)m (x-b)n f '(x) = m(x-a)m-1 (x-b)n + n(x-a)m (x-b)n-1 f '(x) = [(x-a)n-1 (x-b)n-1 ] [(m)(x-b) +(n)(x-a)] And this is as far as I got.

hello there! i need to get the integer part of the output of a division in MATLab i.e. 23/5=4 (and the remainder is 3) what function should i use?

What is the best way to redefine Greatest integer function as a piecewise function for example f(x) = [ 2x - 3 ] , -2<= x <= 1

Hello every one, I need help on some mathematica run program. Suppose the following: 1) 2=<t=<1000 2) r=3+2Sqrt[2] 3) k=(r^t+r^(-t)-20)/4 4) n=2k+4 5) x=n/2-(r^t-r^(-t))/2Sqrt[2] I need to run the program For[t=2,t=<1000,t++ and only print if it found any...

I am doing a problem where I am to determine the probability that the number of students wanting a new book is within two standard deviations of the mean. μ +- 2δ comes out with a non integer number, in which I have to use to find probability. The equation to find probability uses the factorial...

Homework Statement Suppose a, b ε Z. Prove that any solution to the equation x^3 +ax+b = 0 must either be an integer, or else be irrational. Homework Equations Not sure if this is right but x = m / n where m divides b and n divides 1 The Attempt at a Solution So far i think i...

I'm trying to find if a number is odd or not, basically if X % 2 = 1. Can this be expressed through some function? Like the sum of 1 + 2 .. +n is n(n+1) /2 Or as a Riemann sum? I'm trying to add only the odd numbers from a random set of N integers to a sum.

z=6*e2,5i Can anyone explain me ? The imaginary part = 3,59 and real part = -4,81 I tried e(x) = cos x + i sin x, but it does not help me.

Can somebody tell me how to find one sided limits for greatest integer function, say Lim x->n-, [[x/2]]. that is limit x approaches n from left of [[x/2]] where [[]] represent greatest integer function and n is any integer. I know how to find one sided limits for simple [[x]].

Hey all, I am doing a Schwarz-Christoffel transformation and I am trying to calculate the integral analytically using the residue theorem. My integral is the following: \int^\zeta _{\zeta_0} (z+1)\frac{1}{(z+2.9)^{{b_1}/\pi}{(z-0.5)^{{b_2}/\pi}}}dz This has two poles at -2.9 and 0.5. b_1 and...

Homework Statement Argue that (17^4)*(5^10)*(3^5) is not the square of an integer. Homework Equations N/A? The Attempt at a Solution Do I break these up, and show that each is not a square? I'm not sure if that would be correct, but sqrt(17^4)=289 * sqrt(5^10)=3125 *...

What is the integer X which satisfies 10^x < 1/2 X 3/4 X 5/6 X 7/8 X ... X 99/100 < 10^(x+1) ? Could I get some help? This contest allows the use of calculators but I still can't think of the right approach.

hello, I am trying to solve this problem: If w is an even integer, then w^2 - 1 is not a prime number. my current working. prove by contradiction If w is a even integer then w^2 -1 is a prime number. if w = 2x then w^{2} -1 = 4x^{2} -1 I am not sure where to go from here, maybe congruence...

Hi PF, Hoping somebody out there can help me to clear up what is probably a silly misunderstanding of the IQHE: Since the quantized Hall current can be expressed as a property of occupied bulk bands (Chern number) why do we say that the current is carried by the edge states?

Homework Statement If a, b and c are positive integers with (a,b) = 1 and c2 = ab, show that each of a and b is the square of an integer. I've been staring at this problem for a while now and I've got not clues. I don't see the relation between a and b being relatively prime and the rest...

Homework Statement I want to create a program that prints the sum of integers k for k(1-20) ie, k sum 1 1 2 3 3 6 4 10 5 . 6 . . . . . . 20 . in that format Homework Equations The Attempt at a Solution #include <stdio.h> int...

RESOLVED Homework Statement Let a = 123, b = 321. Compute d = gcd(a,b) and express d as an integer combination of ra + sb.Homework Equations This is a question (3.1, page 70 of Michael Artin's Algebra). For those who do not have the book, this problem is relevant to the section on subgroups...

Hi there, So in bragg's law 2d\sin \theta =n\lambda, n needs to be an integer. Can anyone explain why? I mean, what if the extra path 2d that the 'second beam' has is not dividable by a wavelength? Not sure if this is asked before but could not find it! Cheers, Adnan

halfway through my code so its a bit of mess but this is simple what i need to do. I have a JLabel array of 6 labels. a random number is generated, its then split into its digits into a 6 element array of integers. now i need to update the Jlabels with the integer array of digits. my...

I have a quick question. The problem reads: Prove that there is no integer m such that 3x2+4x + m is a factor of 6x4+50 in Z[x]. Now, Z[x] is not a field. So, the division algorithm for polynomials does not guarantee us a quotient and remainder. When I tried dividing 6x4+50 by 3x2+4x +...

I am trying to solve how an integer is simultaneously that is simultaneously a square and a cube number must be either of the form 7k or 7k+1 and I am failing when i work (7k+2)^2, even (7k+3)^2....Can i interpret 7k+1 as 7k+(-1), i think i can't but then i fail in many steps! Also i know that...

What are people's opinion on these two questions? The obvious answer for the first question (5) seems too simple, as it merely stems from the observation that the last number in the first two rows happen to be the average of the first three. I'm not sure if the real solution is this easy...

I'm reading up on some methods to solve differential equations. My textbook states the following: "y_{1} and y_{2} are linearly independent ... since \sigma_{1}-\sigma_2 is not an integer." Where y_{1} and y_{2} are the standard Frobenius series and \sigma_1 and \sigma_2 are the roots of...

Prove that for any non-zero positive integers b,s a = \large \log_x \bigg(\dfrac{ ( -3 + x^{2b} ) \pm \sqrt{(3-x^{2b})^2-4x^{2b}(1-s^2)}}{2x^{2b}}\bigg)\notin \mathbb{Z}. The above expression comes from the result x^a = \dfrac{ ( -3 + x^{2b} ) \pm...

Calculate Natural no. $n$ for which $\displaystyle [\frac{n}{1!}]+[\frac{n}{2!}]+[\frac{n}{3!}]+...+[\frac{n}{10!}] = 2012$ where $[x] = $ Greatest Integer function

I can't seem to find on the web a site that gives the Z cohomology of the infinite dimensional Grassmann manifold of real unoriented k planes in Euclidean space. I am interested in computing the Bockstein exact sequence for the coefficient sequence, 0 -> Z ->Z ->Z/2Z -> 0 to see which...

I am preparing for my Fall bridge to abstract math course and came across following problem: "Prove that there is no odd integer that can be expressed in the form 4j-1 and 4k+1 for integers j and k." If you let P(x) = "x is odd" Q(x) = (\existsj\inZ)(x=4j-1) R(x) =...

Homework Statement Show that negative divisors of an integer, are just the negatives of the positive divisors. The Attempt at a Solution having an integer n and a negative divisor k, we get the positive divisor by multiplying (-1)k, thus each negative divisor of an integer, is the...

Homework Statement I have a thousand random numbers generated between -100 and 100 and want to count the number of occurences of each integer. I know i can use the COUNTIF function, but for so many numbers it takes way too long. Is there a way to create a loop in excel that can do this or...

New formula that can divide by zero to give an integer! Does anybody here know about the Bhartiya New Rule of Fraction(BNRF)? It is capable of dividing by zero! In most elementary terms, we know that division is successive subtraction. For example 6 divided by 3 is 2 because 3 can be...

the number of ordered pairs of positive integers $x,$y such that $x^2 +3y$ and $y^2 +3x$ are both perfect squares my solution...

Let \begin{equation*} A=% \begin{bmatrix} 0 & 1 & \cdots & n-1 & n \\ 1 & 0 & \cdots & n-2 & n-1 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ n-1 & n-2 & \cdots & 0 & 1 \\ n& n-2 & \cdots & 1 & 0% \end{bmatrix}% \end{equation*}. How can you prove that det(A)=[(-1)^n][n][2^(n-1)]? Thanks.

[FONT=Tahoma]A polynomial $f(x)$ has Integer Coefficients such that $f(0)$ and $f(1)$ are both odd numbers. prove that $f(x) = 0$ has no Integer solution

Homework Statement Prove that \lim_{x\to0}\frac{e^\frac{-1}{x^2}}{x^n}=0 for any positive integer n. Homework Equations The Attempt at a Solution I've tried using a combination of induction and l'hopital's rule to no avail. Perhaps I am over complicating it? All help is...

How to prove that if $\varphi$ is the characteristic function of an integer valued distribution, then the probability mass function can be computed as $ p(k) = \frac{1}{2\pi} \cdot \int^{\pi}_{-\pi} e^{-ikt}\varphi(t) dt \;,\forall k \in \mathbb{Z} $ I would be really grateful if you could help me.

Homework Statement if n is a positive integer than √(4n-2) is irrational. Homework Equations The Attempt at a Solution √(4n-2) Assume is rational then by definition of rationality √(4n-2)=p/q for some integers p,q where q≠0 so √(2(2n-1))=p/q by factoring out the...

Homework Statement (E): x^2+y^2=6+2xy+3x The Attempt at a Solution x^{2}+y^{2}=6+2xy+3x\Longleftrightarrow x^{2}-2xy-3x+y^{2}=6\Longleftrightarrow x^{2}+x(-2y-3)+y^{2}=6 Any further help to find the answer??

This is probably a silly question, but it is not really clear to me whether De Moivre's theorem of raising a complex number to the nth power only work if n is an integer value? E.g. if I try to raise (2-2i) to the power of 3.01 then my manual calculation get a different result than my...