Integer Definition and 606 Threads

prove that for any integer n, n^{2} \cong 0 or 1 (mod 3), and n^{2} \cong 0,1,4(mod 5)

Can someone explain why if an invertible matrix A has det = 1 and all integer entries, its inverse also has all integer entries? det(A) = 1 means that if you apply the big formula (permutations) the sums of the entries add up to 1. But what does that have to with having integers in its...

For example a number whose domain would be all positive would be described as a number k, where k > 0. How would you describe a number that is an integer, ie not 1.4, 7.666 et cetera. I can't think of a way to define this mathematically (or a way that includes any number of digits). I know...

Like for example Prompting message reads. "Please enter a positive value" Example: Please enter a positive value: 234.7 Rounded to the nearest integer the number is: 235 Please enter a positive value: 10.3 Rounded to the nearest integer the number is: 10 What I have...

Homework Statement Use proof by contradiction to show that every integer greater than 11 is a sum of two composite numbers. The Attempt at a Solution The question sounds a bit awkward for me since for the numbers I have tested so far. The number can be consists of 1 prime 1 composite or...

I was given this homework today and without much explanation from the teacher , I can't find anything similar in my book, 1.- [[ x]] = [[y]] find outside domain/range , argue inclusion or exclusion 2.- compare and contrast (1) y=[[2x]] (2) y=2[[x]] (3) y= [[x/2]] 3.- state domain and...

Dear all, I have a problem with Fortran 90. I want to declare an integer which is enable to support till numbers such as Avogadro number (6.022*10**23). I use "Microsoft Fortran PowerStation 4.0". Can anyone can help me please? Regards,

I have a doubt about electric flux. It is said to be the no. of field lines passing through a given area. But then we integrate it as: \int\vec{E}.\vec{ds}=\Phi However, bein the number of field lines does it not have to be an integer?

find lim (-1)^[x] x->2 [x] is the greatest integer function -> means tends to thanks to any help.

I am posting an integer factorization algorithm that I have developed. I am hoping for feedback on any obvious flaws that I might have missed before writing a computer programme to test it out. Thanks in advance Visu

Homework Statement Hi, I hope someone could help me, I have been trying to solve this problem with FFT in matlab, why?, because my teacher gave it as homework. The problem is the following. Obtain the value of the following integer using FFT: Homework Equations the integer goes...

Hi, I hope someone could help me, I have been trying to solve this problem with FFT in matlab, why?, because my teacher gave it as homework. The problem is the following. Obtain the value of the following integer using FFT: the integer goes from [-infinte, infinite], and the function is...

we must obtain 'N' and a(i) i=1,2,3,....,N on condition that the product a(1)a(2)a(3)...a(N) is the highest possible a(1)+a(2)+a(3)+...+a(N)=73 every a(i) is positive here N (this is the hardest part) is not known and must be calculated

[SOLVED] A limit Homework Statement How do you show that \lim_{x\rightarrow a}\frac{e^{-a^2/(a^2-x^2)}}{(a^2-x^2)^{2m}(x-a)}=0 for 'm' a positive integer and 'a' a real number >0??This is a type 0/0 indeterminate form but l'Hospital's rule is not helpful because when you differentiate the...

I'll try my luck here: How do you determine whether an integer coefficient single variable polynomial has at least one real root?

Homework Statement Prove that for all x there exists and x if it is an element of the positive integers, then there is an integer y and an integer z. Homework Equations The Attempt at a Solution I know that the contrapositive would be "If there is not an element of the positive...

Homework Statement Can someone explain the notation of the integer ring(Z)? My friend's in Math 100 and has questions on Z. I have never heard of ring's before and I'm at a loss to help him. From what I've gathered Z is a set of all integers. They ask for the invertible elements in different...

Homework Statement I don't know where to start on this question - could someone please point me in the right direction so i can look up the method. Q: Find integers x, y such that 45x + 63y = 99. Can we find integers s, t such that 45s +65t = 80? Either find them or prove they cannot exist.

let n be a-positive integer. Prove that a and c leave the same remainder if and only if a - c =nk for some integer k.

Homework Statement Prove that the square of any integer a is either of the form 3k or of the form 3k+1 for some integer k.Homework Equations The Division Algorithm: Let a,b be integers with b>0. Then there exists unique integers q and r such that a = bq + r and 0<=r<bThe Attempt at a Solution...

can anyone tell me how to solve for integer solutions of [x]*[y]=x+y tell the interval of its non integral solutions pleazzzzzzzzzzzzzzzzzz...

Could anyone please answer this You are confronted with the following formula: A * [(B + C)(D - E) - F(G*H) ] / J = 10 Knowing that each variable is a unique, single-digit, nonzero number, and that C - B = 1, and H - G = 3, what is the number ABCDEFGHJ, where each letter is a digit...

how does one go about finding integer solutions for an equation such as this? Is it easier to merely find how many solutions? y^2 = x^3 + n, n is some integer.

This is a problem from Terence Tao's book, and I cannot locate the solution anywhere, so I thought I'd post it here. 1. Homework Statement X^4+131=3y^4, Show that the equation has no solutions when x and y are integers. Homework Equations None? Not sure. The Attempt at a...

Homework Statement How would you prove using number theory that C(n,m) is an integer where n => m =>1? Do you need the Chinese Remainder Theorem? It seems like it should follow easily from what C(n,m) represents but it is hard for me for some reason. Homework Equations The Attempt...

one of the "maths challenge" questions. one of the only ones i couldn't do :S I've tried for a good number of hours, but havnt found a way to do it. I feel any more time would just be brute forcing it which i wouldn't have time for in the exam anyways. hope you can help Homework Statement...

Homework Statement I need the eigenvalues of [[3, -1][-1, 1]] (ie [[row1][row2]]) The Attempt at a Solution A-xI = [[3-x, -1][-1, 1-x]] so I get the characteristic polynomial x^2-4x+2=0 from det(A-xI)=0 Is this correct? Because I won't get integer eigenvalues from it

Homework Statement Let n and k be positive integers. Show that k^{1/n} is either a positive integer or an irrational number. The Attempt at a Solution I set q = k^{1/n}. Then I set q = \frac{m}{p} . (Where m and p don't have common factors.) Then m^n = k * p^n . So then k is a factor...

"Reflection of an Integer" I haven't encountered this before. I'm not sure how to approach it. At this point it's not even clear to me why the result should only be divisible by one number in *every* case. The reflection of a positive integer is obtained by reversing its digits. For...

Homework Statement Is it there a method to find out if a polynomial has no integer roots? The Attempt at a Solution I tried the division of polynomials, as well as the Horner's Method, but no luck.

Hi,.. using a Sturm or other sequence, could we find how many integer roots have the Polynomial K(x)= \sum_{n=0}^{d} a_{n}x^{n} where all the 'a_n' are integers (either positive or negative)

Let be a open curve on R^2 so x^{n}-c-ky=0 where k,n and c are integers, are there any methods to calculate or at least know if the curve above will have integer roots (a,b) so a^{n}-c-kb=0 ?? or perhaps to calculate the number of solutions as a sum (involving floor function) over integers of...

Why are the atomic weights of elements not integers and how many grams would there be in 1 amu (atomic mass unit) of a material? I know these are trivial questions but it's been a long time since I left school! Thanks. -SK

Is there a quick way to find integer values of x that give integer values for y? (x^2-R)/(P-2x)=y sqrt(R) rounded down<x<P/2 an equivalent equation is x^2+Px+R=y y= a perfect square sqrt(x^2+Px+R)= integer P and R are integer values. They are very large...

Homework Statement Prove that if m is a positive rational number, then: m + 1/m = integer Only when m = 1 Homework Equations Don't know any The Attempt at a Solution That's the problem, I don't know where to start. I have tryed a few things, but none of them works out for...

The other day, Mack was preparing a table consisting of integer Fahrenheit temperatures (F) which yields integer Celsius (C) equivalent upon conversion. He noted that F= 527 gave the corresponding C value as 275 and realized that, he could have simply moved the first digit in F to the end to...

hi guys.. Does this statement require a proof? It seems pretty obvious to me. "prove that there is no integer between n and n+1 where n is an integer." Also if it does require a proof, what I need to show? Just few hints will suffice. thanks jitendra

Homework Statement Q1 [|x+2|]=2[|x|]-3 Q2 If f is even and g is odd, is fog even, odd or neither Homework Equations The Attempt at a Solution Q1 Not sure. Can someone please give me a start on this? I think if I knew some properties of greatest integer functions I could work...

i want to prove that for every positive integer k, we can find such a positive integer n, such that k divides n and n is only composed of the digits 0 and 3. i don't have any idea how to approach this problem. any help will be appreciated. thanks in advance.

Homework Statement Use mathematical induction to show that given a set of n\,+\,1 positive integers, none exceeding 2\,n, there is at least one integer in this set that divides another integer in the set. Homework Equations Mathematical induction, others, I am not sure The...

n=a²+b²-c², show that it's true for any integer n,a,b,c its an exercise of the math olympiad of my city... i know i should have posted at least a bit of my work, but i think there is a trick to solve this category of problems that i dnt know...where should i start?

let be a 2 dimensional symmetryc form: z=f(x,y)=ax^{2}+bxy+cy^{2} depending on the values of a,b and c we'll have an elipse , parabole and hyperbola or circumference,my question is are there any geommetrical methods to find integer points (x,y) satisfying the equation z=constant ...

A while back, I found an online applet that was located on the front page of the mathematics department website for some American university. The problem is that I can't remember which university it was, and I'm not succeeding in several searches. Basically, the way it worked was, you type...

Consider all functions g from the positive integers to the positive integers such that: (a) For each positive integer p there exists an unique positive integer q such that g(q) = p; (b) For each positive integer q, we have g(q+1) as either 4g(q) -1; or; g(q) -1. Determine the set of...

Determine all possible integer solutions (p,q) of the equation: sqrt(p+ sqrt(p+ sqrt(...(p + sqrt(p))...))) = q The "sqrt" symbol in the above relationship is repeated 1964 times. Note: sqrt(x) stands for the square root of x.

I just need a push in the right direction for this one. The problem is: A phone company charges this amount for the first minute and that amount for each additional minute. If someone talks for 3.1 minutes, they are charged for 4 minutes. Make a formula, blah blah blah... Anyway I'm having...

Ok, my question is: Show that if ab == 1 mod m, then ord(m)a=ord(m)b (Note that == means congruent) and ord(m)a means the order of a mod m I know that if a^k==1 mod m, then the ord(m)a is the smallest integer k such that the congruence holds. For example, ord(10)7=4 since 7^4==1 mod...

What is the notation for the statement "for some integer n"? What is the notation for the statement "for some integer n"? Is it \forall n | n \in Z Or is it \{n | n \in Z \} Or is it something else? | does mean "such that", doesn't it?

Hello everyone. I'm trying to set this problem up to prove by induction but having some issues. Suppose that for some Predicate P(k), you first prove that P(1) is true, and then you do the following. You prove that, for every positive even integer k, if P(i) is true for all odd integers i...

Hello everyone. I'm suppose to prove this but I'm having troubles figuring out how u find "distinct" integers. Meaning they can't be the same number. i figured it out they just wanted integers though. Here is the question: There are distinct integers m and n such that 1/m + 1/n is an...