Integer Definition and 606 Threads

given $h+k=2016$, and the two roots $\alpha \,\, and \,\, \beta $ of equation $x^2+hx+k=0$ are all integers , please find the value of: $h,k,\alpha \,\, and \,\, \beta$

I learned Fortran from ancient people who disregard modern standards. As such, my code consists mainly of that older syntax. I am wondering how well this meshes with current Fortran environments, specifically regarding double precision calculations. This comes up mainly because I have been...

Solve the following equation for integer solutions: $a^2(b-2)+b^2(a-2)+28=0$

Solve for integers $a,b,c$ given $a^2+b^2+c^2 + a + b+ c = 1$

At work I am writing a somewhat complex piece of software, and inside it at some point I have to solve the following problem: I have several "streams", each of which has equally spaced points according to a proportionality factor 'a', i.e. X=a*n. Each stream has a different 'a'. As an example...

Dear all, How to deal with negative integer factorial functions? I mean what expression formula can be substituted for this?

Homework Statement If ℤ[x] denotes the commutative ring consisting of all polynomials with integer coefficients, list all the elements in ℤ[x] that have a multiplicative inverse in ℤ[x]. Homework Equations Multiplicative inverse if rs = 1 where rs ∈ R (rs are elements of the ring)...

Homework Statement Let a and n be positive integers. Prove that a^(1/n) is either an integer or is irrational. Homework EquationsThe Attempt at a Solution Proof: If a^(1/n) = x/y where y divides x, then we have an integer. If a^(1/n) = x/y where y does not divide x, then a = (a^(1/n))^n =...

Say I apply a raising operator to the spin state |2,-1>, then by using the the equation S+|s,ms> = ћ*sqrt(s(s+1) - ms(ms+1))|s,ms+1> I get, S+|2,-1> = sqrt(6)ћ|2,0> Does this correspond to a physical eigenvalue or should I disregard it and only take states with integer multiples of ћ as...

Evaluate $$\left\lfloor{\frac{2014^3}{(2015)(2016)}+\frac{2016^3}{2014(2015)}}\right\rfloor$$.

Determine all triples of positive integers $x,\,y,\,z$ such that $z\ge y\ge x$ and $x+y+z+xy+yz+xz=xyz+1$.

Find all positive integer solutions to: $xyzt-2xyz-xyt+2xy+zt-2z-t=12$

Homework Statement Write a program that will square the input positive integer represented as a string. Homework Equations 3. The Attempt at a Solution [/B] Is there another way of squaring a string number instead of multiplying it by itself? Something like a pow() function for strings? If...

Hey! :o I want to prove the following implication: $$k \in \mathbb{Z} \Leftrightarrow ce^x-1 \mid c^ke^{kx}-1$$ For the direction $\Rightarrow$ I tried the following: $k >0$: $$\sum_{i=0}^{k-1} (ce^x)^i=\frac{(ce^x)^k-1}{ce^x-1} \\ \Rightarrow (ce^x)^k-1=(ce^x-1)\sum_{i=0}^{k-1}...

Solve for positive integers $x$ and $y$ where $x^2+x=y^3+y^2+y$.

Homework Statement How many non-negative integer solutions are there to the equation x1 + x2 + x3 + x4 + x5 < 11, (i)if there are no restrictions? (ii)How many solutions are there if x1 > 3? (iii)How many solutions are there if each xi < 3? Homework Equations N/A The Attempt at a Solution...

I am confused about the concept of a mole. Avogadro's # says that 1 mole has 6.023*10^23 particles. Does it make sense to talk about moles in a non-integer sense? For example, can you say that 1/2 mole has 1/2*(6.023*10^23) particles?

Homework Statement I am to write a program that has its user enter 100 character or less and determine if the line is a palindrome or not. I must use pointers one that starts at the beginning and one at the end of the array that must work their way in until they meet.(I'm also having trouble...

Find all the positive integers $x$ such that $\dfrac{1}{4}<\dfrac{1}{x+1}+\dfrac{1}{x+2}+\dfrac{1}{x+3}<\dfrac{1}{2}$.

Determine all integer pairs of solutions for $(a,\,b)$ such that $\sqrt{a-\sqrt{b}}+ \sqrt{a+\sqrt{b}}=\sqrt{ab}$.

write a c programs Take integer and find all divisors/Factors , print is it prime or not? and how many divisors contain print it? how to solve in one program and how many divisors/Factors contains my code: #include<stdio.h> #include<conio.h> #include<math.h> int main() { int number,i...

Find the positive integer numbers $a$ and $b$ such that $65(a^3b^3 + a^2 + b^2) = 81(ab^3 + 1)$.

Write a “C++” program to read any integer number and print each digit into word. I went like this # include <iostream.h> #include <conio.h> void main(){ int a,b,c,d; clrscr(); b=a cout<<"Enter any number"<<endl; cin>>a; c=a%10; d=a/10; I am not getting further logic. someone was saying for loop...

Hey! :o I want to prove the following lemma: Let $F[t,t^{-1}]$ be the ring of the polynomials in $t$ and $t^{-1}$ with coefficients in the field $F$ and assume that the characteristic of $F$ is zero. Then for any $n$ in $F[t, t^{-1}]$, $n$ is a nonzero integer if and only if $n$ divides...

So I just completed a simple exercise that converts all letters of a string to upper case letters. The program works but it comes with the warning: comparison between signed and unsigned integer expressions [Wsign-compare]. What does this mean? While whatever is causing the warning does not seem...

Homework Statement For a positive integer ##n##, let ##a_n=\frac{1}{n} \sqrt[3]{n^{3}+n^{2}-n-1}## Find the smallest positive integer ##k \geq2## such that ##a_2a_3\cdots a_k>4## Homework Equations The restrictions are the only relevant thing I can think of The Attempt at a Solution I have...

Homework Statement ##x_1+x_2 \cdots x_{251}=708## has a certain # of solutions in positive integers ##x_1 \cdots x_{251}## Now the equation ##y_1+y_2 \cdots y_{n}=708## also has the same number of positive integer solutions ##y_1, \cdots y_n## Where ##n \neq251## What is ##n## Homework...

Homework Statement Let ##x,y,z## be positive integers such that ##\sqrt{x+2\sqrt{2015}}=\sqrt{y}+\sqrt{z}## find the smallest possible value of ##x## Homework Equations Not even sure what to ask I'm trying to learn number theory doing problems and look up information by doing the problems...

Why is it necessary that the principal quantum number of a Hydrogen atom problem in Quantum mechanics must be an integer?Couldn't it be any fraction?

Dear Everyone,I would like some help to get start with a proof. A problem states, "if p is an integer, show that p is even iff p^2 is even."I know that p is the an integer. Let p be an integer. $p=2m$, where m is an integer.Thank you for your help CBarker

$A=\sqrt{1^2+\dfrac{1}{1^2+2^2}}+\sqrt{1^2+\dfrac{1}{2^2+3^2}}+\sqrt{1^2+\dfrac{1}{3^2+4^2}}+---+\sqrt{1^2+\dfrac{1}{2011^2+2012^2}}$ please find an integer S most close to A and less than A

I am trying to define a real number as follows: real*8 r r=2.5*10**20 This results in the following warning: r=2.5*10**20 1 Warning(131): Integer overflow at 1 First off, I am not even declaring it as an integer, yet the warning is named as such. After searching around for...

$A=\sqrt{\dfrac{1}{\sqrt[3]9-2}+2\sqrt[3]9}$ find an integer $B$ most close to A

Homework Statement I am a hobbyist looking for solutions to ax^2 + bx - cy^2 - dy = 0 where all variables are integers and are non-zero. Is there a method of doing this effectively? Homework EquationsThe Attempt at a Solution I can look at the numbers produced by ax^2 + bx vs cy^2 + dy and see...

Prove that for any integers $x,\,y,\,z$, there exists a positive integers $n$ such that $\sqrt{n^3+xn^2+yn+z}$ is not an integer.

Not homework but given the question it probably fits here best Given the following equation $$x^2+138x+317=y^2$$ How do you find the integer solutions? For example wolframalpha has the solutions. but I cannot see how they are derived http://www.wolframalpha.com/input/?i=x^2+138x+317=y^2 By...

Why is π/2∫3π/2[cos-1t].dt = π/2∫3π/2-1.dt? [.] denotes the greatest integer function. Is it because [cos-1t] = -1 in t ∈ [π/2,3π/2)? But [cos-1t] = 0 for x = 3π/2. So we have one 0 along with all the -1's in (π/2,3π/2]. So how can we substitute [cos-1t] = -1 for every x in (π/2,3π/2] even...

Hi, so I'm trying to use the following if statement: if (sum(i,j) <=1.0 ) then sidash=(si)*(Death) else if (1 <= sum(i,j) <= 2) then sidash=(si)*((sqrt(2.0)+1.0)*(2.0-sum(i,j))*(Death)+(sum(i,j)-1.0)*(Survive)) else if (sum(i,j)<=3 .and. sum(i,j)=>2) then...

hey guys, I wonder if you could help me... i cannot factor the integer 2896753 by pollards p-1 method and the quadratic sieve .

Just a simple question -- can the dimension of coupling constant be a rational number or should it always be an integer? The question arose when I was trying to construct a Lagrangian with an interaction term involving two spin-1 particles and a fermion. The dimensions add up to 7/2, which...

Prove that the product of 5 positive integers $(p,\,q,\,r,\,s,\,t)$ satisfying the equation $pqrst=5(qrst+prst+pqst+pqrt+pqrs)$ is an odd integer.

Assume that I have absolutely no clue to what is the formula used to generate a sequence. How do I know what kind of formula that is? (Exponential / Linear / Polynomial / etc) Also assume that there is only 1 formula that generates the sequence. I have read somewhere before that: f'(x) ~...

Q:Explain this phenomenon by finding a sequence of integers a_i, defined by a recursion relation similar to the Fibonacci sequence, such that a_n = (2 + √ 3)^n + (2 −√3)^n. Make sure to explain why constructing such a sequence proves (2 + √3)^50 is close to an integer, though you needn’t analyze...

I mean why is f=ma? why not m0.123a1.43 or some random non integers? I hope you understand that my doubt doesn't limit just to force or energy or velocity e.t.c. it also extends to area of a square,circle e.t.c and all other formulae i think whole thing starts with direct proportionality.

If $\dfrac{1}{9!1!}+\dfrac{1}{7!3!}+\dfrac{1}{5!5!}+\dfrac{1}{3!7!}+\dfrac{1}{1!9!}=\dfrac{2^x}{y!}$ find $x,\,y$ where they are positive integers.

If $x,\,y,\,z \in Z$ and that $z\ge y \ge x$ and also, $x+y+z=-3$ $x^3+y^3+z^3-20(x+3)(y+3)(z+3)=2013$ evaluate the value for $3x+y+2z$.

Let $P(x)$ be a polynomial with integral coefficients. Suppose that there exist four distinct integers $x_1,\,x_2,\,x_3,\,x_4$ with $P(x_1)=P(x_2)=P(x_3)=P(x_4)=5$. Prove that there is no integer $a$ with $P(a)=8$.

f(n) is defined as 11x22x33...xnn Then it seems as if f(n)/(f(r).f(n-r)) is always an integer for 0 < r < n. I tried a few cases. Its true for them. Is it always true? I cannot seem to figure out any ways to prove it.

Prove that the equation $x_1^3+x_2^3+x_3^3+x_4^3+x_5^3=k$ has an integer solution for any integer $k$.

Greg Egan just proved something nice: the E10 lattice, famous in string theory and supergravity, can be described as the lattice of self-adjoint matrices with integral octonions as entries! I'm not sure this result is new, but I've been wanting it for quite a while and haven't seen it...