Integer Definition and 606 Threads

Homework Statement The question is not really a question from a book but rather a statement that it makes : it says " Obviously the least divisor[excluding 1] of an integer a is prime if a itself is not prime." I kind of believe this statement but I'm having trouble proving the general case...

Homework Statement find the least positive integer n for which 5^{n} \equiv 1 (mod17) or 5^{n} \equiv -1 (mod 17) Homework Equations The Attempt at a Solution I really don't understand and method to doing these problems as I can't use a calculator and I can only work out...

Consider the region A in the complex plane that consists of all points z such that both \frac{z}{40} and \frac{40}{\overline{z}} have real and imaginary parts between 0 and 1, inclusive. What is the integer that is nearest the area of A? Let z = a + bi and \overline{z} = a - bi a = real part...

hi all, i have the following code: do n = ninit,nlast character(len=20) :: filename integer :: n do n = 1,600 write (filename, "I0") n open (unit=110,file='wave'//trim(filename)//'.dat',action = 'write',status = 'old') do i = iinit+1,ilast-1 !boundary condition...

What is the probability that a number selected from 0-9 will be the same number as one randomly selected from 0-4? Relevant equations: $$P(A \cap B) = P(A)*P(B|A)$$ I used the equation above, using A as the event that the number selected from 0-9 will be between 0 and 4, and B as the event that...

If there is a cloud of electrons around an atom than why can't there be orbitals between 1 and 2 or between 2 and 3. I know the probability of an electron being between certain nodes decreases as they approach them but why as the probabilities go away from the perfect orbital do they not become...

In:list5 = Import["Composites.csv"]; (*imports a list of odd integers each less than 1000000*) Timing[f=Compile[{{Caa,_Integer},{S0,_Integer},{S1,_Integer},{Co,_Integer}}, Module[{xCo=Co,xS0=S0,xS1=S1,Temp},While[Temp=Mod[6 xS1-xS0-6,Caa];xCo>0&&Temp>=1, xS0=xS1;xS1=Temp;xCo--]; xCo]]...

This has to do with number theory along with group and set theory, but the main focus of the proof is number theory, so forgive me if I'm in the wrong place. I've been struggling to understand a piece of a proof put forth in my book. I know what the Gaussian integers are exactly, and what a...

Hi, I have three situations where might be overflow is occurring. I need to write test cases to resolve this problem. I don't know how to continue after this, please anyone have suggestions to overcome this. Please help me.

It seems that there is a possible ambiguity in the number of significant digits if there are trailing 0's, but no decimal point or overline or underline. Specifically, I am looking at the definition of the second, which the Halliday & Resnick book has listed as 9 192 631 770 So is this 9...

Homework Statement This is taken from an answer book that I have. I don't understand the bolded step. Can someone explain it to me?Suppose x = p/q where p and q are natural numbers with no common factor. Then: pn/qn + an-1pn-1/qn-1 + ... + ao = 0 and multiplying both sides by...

Hello everyone, I've been trying to figure out how to obtain the multiplicative inverse of an integer in Zn in Mathematica but I haven't found a way. Is there a way to do this anyone can help me with?

I want to prove that the square of any integer is in the form of 4n or 4n + 1. I know that when we square any integer greater than 2 the result will be either divisible by four or four divides into the integer and leaves a remainder of one. How would I begin proving this in the most...

Homework Statement a)Determine at least three limit points for the set {sin(n): n a positive integer} b)How many limit points does the set {sin(n): n a positive integer} have? The Attempt at a Solution For a it seems that it wouldn't have a limit point because sin(n) would not converge to...

Hi there, It is clear that \lim_{n\to\infty }\frac{1}{n}\left[\frac{n}{3}\right]=\frac{1}{3}. But the problem that I could not get a formal proof! Thank you.

My first post on these forums, was referred here by a friend of mine. Thanks in advance! Mind that this question is coming from a BA in psych's worth of understanding: If I understand correctly, estimations of error margins are based on the relationship between a population and a sample of...

I know the Cartesian product for an algebraic structure: A x B = {(a,b): a ∈ A, b ∈ B} Which naturally gives An = {(a1, a2, ... , an): ai ∈ A ∀ i} Some of the time, at least we can also have a non integer n. For example [A x A x A]2/3 = A x A. Is there any way of continuing the...

Homework Statement prove that each nonzero integer may be uniquely represented in the form e0 + e131 + e232 + ... + ek-1ek-1 + ek3k where ek =/= 0 and each ek = -1, 0, or 1. Homework Equations The Attempt at a Solution I feel like this has to do with the basis representation theorem because...

Homework Statement b^2 = a b is a rational number a is an integer prove that b is an integer. This is self assigned, but I think this is the appropriate place to put my question. Homework Equations see above The Attempt at a Solution Is this legitimate...? Since b is a...

So I have a simple selection sort function written. It takes an array of type [FONT="Courier New"]double as the array to be sorted. If I declare the array to be of type [FONT="Courier New"]int in my [FONT="Courier New"]main program and then pass it to my sSort function, it gets mad. There must...

Homework Statement Work out the order of the following elements; 33 \in Z_{36}The Attempt at a Solution It's probably really simple. But this only happens when an integer times 33 is divisible by 36. That is; 33n = 36m Which I can re-arrange to find n = 36m/33 Now, I can keep adding...

Say I have the equation a^2 - 10b^2 = 2. So even though this is an equation in two variables and not one, I can still reduce mod P to a^2 = 2 (mod 5) and use the fact that it has no integer solutions mod 5 to conclude the original equation has no integer solutions, correct? Also does this only...

Homework Statement Prove that, for all x, y \in \mathbb{R}, [2x] + [2y] \geq [x] + [y] + [x + y]. Homework Equations I am using [\cdot] to represent the floor function, and \{\cdot\} to represent the fractional part of a real number (\{x\} = x - [x] for real numbers x). We may...

Homework Statement I am stuck on a step from a simple proof in Gelfand's method of coordinates. Here is a link to the part I am confused on. Pg. 44-45...

Whats the easiest way to take an integer in C# and convert it into an array of length equal to the number of digits and each element is a digit from the integer? EG. If I had the integer 12345 I want to convert it to an array like so {1, 2, 3, 4, 5} Thanks AL

Right now I'm watching a US Public Broadcasting Corporation television program entitled: "The Linguists", in which a man (I think he was from Africa, but I'm not even certain of that, as I wasn't even listening until the math stuff surfaced), explaiined his integer progression, which was quite...

Hi everyone. My first post on this great forum, keep up all the good ideas. Apologies if this is in the wrong section and for any lack of appropriate jargon in my post. I am not a mathematician. I have a theory / lemma which I would like your feedback on:- Take a finite set S of integers which...

Hi, I was studying for my upcoming calculus exam and couldn't be sure if I could solve this question: \stackrel{lim}{x\rightarrow0} x [\frac{1}{x} ] If x approaches 0 from left, then 0< x [\frac{1}{x} ]<1 If x approaches 0 from right, then x [\frac{1}{x} ]>1 since x [\frac{1}{x}...

Hello, the problem that I was asked to complete was ; Write a program that inputs a string and reverses it. After the string has been reversed you must convert it to an integer and then take the square root of the integer. (using atoi) My code is as follows: int main () { int i=0,L=50...

Homework Statement For every non-negative integer z, z2 - 3z is an even integer. Prove this statement. So far, I have learned about direct proofs and indirect proofs such as contraposition and contradiction. Homework Equations An integer z is odd when there is an integer a so that z = 2a+1...

It seems as if the charge we have labelled the electron with has simply been inferred by comparing it to the proton, in which case it is pretty much exactly the opposite, so we give the proton and electron charges of +1 and -1 respectively. This is fine, but when we get to the standard model...

Is there a simple way to find the integer values of f(x)=(a+5x)/(6x+1) with a, x integers.

Homework Statement Just as the title said, I need to prove: For any integer n, n2 - 2 is not divisible by 4 by the method of proof by contradiction. Homework Equations (Relevant by division into cases) Even numbers = 2k for some integer k Odd numbers = 2m+1 for some integer m...

Homework Statement 2*[x]-3*[3x]+7=0 Homework Equations solve for x when [x] is the integer part of the number. The Attempt at a Solution To solve it i removed the brackets and got x=1 and then i found the integer part of 1 is 1. Is it correct? If not is there a concept to...

Find all integer solutions to ... Homework Statement Find all integer solutions to \begin{array}{l} {a^2} = a + b - 2c + 2d + e - 8\\ {b^2} = - a - 2b - c + 2d + 2e - 6\\ {c^2} = 3a + 2b + c + 2d + 2e - 31\\ {d^2} = 2a + b + c + 2d + 2e - 2\\ {e^2} = a + 2b + 3c + 2d + e - 8 \end{array} ...

Hello everyone, and thanks for reading. I'm having a difficult time understanding something. On yet another attempt to deepen my quantum mechanics understanding I referred to the widely recommended book of Griffiths. I find the book indeed very good and pretty thorough in it's scope. There...

Hey everyone! I was recently scribbling on paper, and after a series of ideas, I got stuck with a problem. That is, can I find out if there exists some integers A and B such that C=2^{A}3^{B} For some integer C? For an arbitrary C, how do I know whether some A, B \in \textbf{Z}...

Homework Statement I needed to solve this single equation with two unknowns. 199x - 98y = -5 0< x <=99 0< y <=99 I typed the equation into Wolfram Alpha and got an integer solution of: x = 98n + 31 y = 199n +63 when n is an integer Since I know my restriction on x and y I can...

Hello every one, please help me finding the integer zeros for this equation -15x^3+45x^2y-15xy^2+y^3+90x^2-210xy+40y^2-120x+184y = 0 I know that the solution should used by diophantine equation but i don't know ho to solve it, Please help :(

Hello all, I am trying to determine if my machine is 64 bit or 32 bit, according to this site: http://support.apple.com/kb/ht3696" the Intel Core 2 Duo I am using is 64 bit, but when I run the following code #include <stdio.h> int main(int argc, char **argv) { char c; int...

Homework Statement a) 50 b) 23 Product of the hexadecimal unsigned 8-bit integers Homework Equations Step Action |||||||||| Multiplicand ||||||| Product/Multiplier 0 Initial Vals ||||||||| 101 000 ||||||| 000 000 010 011 The Attempt at a Solution How...

Hi, I am looking for an explanation, if any, on why every integer square leaves remainder 0 or 1 on division by 4. Appreciate your time and help bluemoon2188

Homework Statement Find the numbers, if any, where the function is discontinuous. f(x) = [[x - 2]] The attempt at a solution function is discontinuous for all integer values of x. I know that this is the obvious answer, however I am required to explain this in clear mathematical...

Homework Statement Consider the following puzzle. You are to choose 4 three-letter "words" from the following list: ECB EFH BEJ GGE HIJ CDE GEG CBJ For each word, you earn a score equal to the position that the word's third letter appears in the alphabet. For example, ECB earns a score...

bosons have integer spin, fermions have half spin, what does that mean? why bosons (integer spin) is able to avoid pauli's exclusion principle?

I realize that this might seems to be a strange question, but after doing some coding i realized the following. to brute force the factorization of all numbers less than one million takes around 665 million tests (i.e. does this number divide the original). to do it "smarter" (least i...

I'm not sure at all how best to approach this problem. Basically, the application is for practicing mental arithmetic. Most of the features are pretty easy, with the exception of division, which is the topic here. I accept a minimum and maximum for the first and last numbers in the division...

"assignment makes pointer from integer without cast" elephant* get_elephants() { elephant *current, *first; int response; /* create first node */ first = (elephant*)calloc(1,sizeof(elephant)); /* THIS LINE */ current = first...

I am trying to understand how I can find the square root of a large prime number in the form of an integer value, the portion after the decimal is irelevant. The numbers I wish to compute range around 188 multiplied by 3 to the power of 6548 plus 1, as an example. so let's say in excess of...

Find the form of all n in N satifying tow(n)=6. (sorry don't know how to write this Tex). What is the smallest positive integer n for which this is true? tow(n)=6 so 6=(1+a1)(1+a2)----(1+ak) where n=p1^a1p2^a2---pk^ak