Integer Definition and 620 Threads

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...

Consider the square root operation. Suppose an integer numbers i > 0 as input variable. Design an algorithm which calculates the greatest natural number less than or equal to the square root of the input variable i. can smby pls explain to me what does this ques mean??if possible explain...

hi... I was thinking... is there any formula that inverts int numbers? like 21 transforms into 12... I have found an algorithm that do this... but I want to know if exists any formula to it... thx...

I am in discrete math class right now and trying to get the sets of numbers straight. So, does the set of integers include 0? Is it ok to use 0 in proofs, that makes finding a counter-example a lot easier and disprove a statement about all integers. Was just wondering if that is legal...

How do I show that \sum_1^n\frac{1}{k} is not an integer for n>1? I tried bounding them between two integrals but that doesn't cut it. I know that \sum_1^n\frac{1}{k}=\frac{(n-1)!+n(n-2)!+n(n-1)(n-3)!+...+n!}{n!} but I can't get a contradiction.

When plucking a string on an instrument, are all the overtones heard produced by the string itself (assuming all other strings are muted)? Would plucking the string without muting the others make a significant different? Another thing, why aren't all overtones integer multiples of the...

Is it appropriate to say that Any Distance=Planck Length * integer value? If not, why is it so?

I'm having trouble with this: Prove that if P is a linear map from V to V and satisfies P^2 = P, then trace P is a nonnegative integer. I know if I find the eignevalues , their sum equals trace P. But how do I find them here? any thoughts? Thanks

\begin{gathered} \forall p,q,r \in \mathbb{N}\;{\text{where }}p > q > 0, \hfill \\ \exists \left\{ {a_0 ,a_1 , \ldots ,a_n } \right\} \subset \left\{ {0,1, \ldots ,p - 1} \right\} \hfill \\ {\text{such that }}r = \sum\limits_{k = 0}^n {a_k \left( {\frac{p} {q}} \right)^k } \hfill \\...

I am interested in the following number which is obtained by concatenting the binary representations of the non-negative integers: .011011100101110111... i.e. dot 0 1 10 11 100 101 110 111 ... This is a little bigger than .43 and I assume it irrational since no pattern of bits repeats...

I have two problems I'm working on that I can't figure out. Could anyone please help? 1. show that if p and q are distinct odd primes, then pq is a pseudoprime to the base 2 iff order of 2 modulo p divides (q-1) and order of 2 modulo q divides (p-1) I've been trying this proof by...

If n is a positive integer such as 2{\leq}n{\leq}80 For how many values the expression \frac{(n+1)n(n-1)}{8} takes positive and integer values? I solved it that way... \frac{(n+1)n(n-1)}{8}=\frac{(n^{2}-1)n}{8} (n^2 - 1)n must have 8 as one of its factor. Either n is a...

Is there an integer n such that \sqrt{n!+n}-\sqrt{n!} > 1 ?

Since one can construct the length of a non-integer square root by drawing accurate triangles, and can draw a circle with a circumference of pi, then shouldn't one be able to plot corresponding non-integer square roots and pi on a number line? I know these numbers are supposedly irrational, but...

4 to the power of 27 + 4 to the power of 1000 + 4 to the power of x. x is the maximum positive integer and it adds up to a perfect square?

suppose you have 3 integers. if the intergers are a mixture of odd and even integers, then why does the sum always equal an odd number?

Can't figure it out Prove that if n is an odd positive integer, then one of the numbers n+5 or n+7 is divisible by 4 My thoughts I don't know if this is right- Multiply n+5 and n+7, because if one of them is a multiple by 4 then shouldn't their product be divisible 4

Count the number of integer solutions of (rather, # of integer lattice points such that) n+\sum_{k=1}^{n} \left| x_{k}\right| \leq N Not homework, so no rush. I have worked it through before with a prof., but he's so brilliant I didn't understand much of anything he said :redface: . His...

Please Help... Riemann Please Help! To compute the Riemann integral of f:[0,1]->R given f(x)=x^k where k>1 is an integer 1. Let m>2 and define q_m= m^(-1/m) Let P_m be the partition of [0,1] given by P_m=(0< q_m^m < q_m^(m-1)< ...< q_m <1) Explicitly evalute L(f,P_m) and U(f,P_m) 2. Show...

This should be a simple question to answer… I’m doing a high school correspondence course, Algebra 2 and I’m trying to understand the “greatest integer function” which apparently has something to do with Step Functions… They give me very little to go one, a few tables and graphs which don’t...

I was in the middle of proving something when I reached a contradiction, that .5 + an integer = an integer. However, this cannot be true, and I'm curious if its acceptable to just say that by definition of integers .5 + an integer is not an integer, or do I have to prove it? Furthermore, if...

I have to answer a homework problem due today that I am not sure how to do the problem reads. "Write a program that calls a void type function to find the maximum of three given integer numbers" We use visual basic studio, any help would be appreciated.

Just a -very quick- clarification Can base-1 represent a nonzero integer ? Is there a base-1 at all? *The digits of binary (base 2) integers contain only 0 and 1's (no 2's allowed). The digits of base-3 integers contain only 0 and 1 and 2's (no 3's allowed). *But base-1 ? Wouldn't it...

Prove that n^3-n is divisible by 6 for every integer n. Is it induction to be used here?...

Hey there, I've been having some problems trying to prove this: "Let p be an integer other than 0, +/- 1 with this property: Whenever b and c are integers such that p | bc, then p | b or p | c. Prove p is prime. [Hint: If d is a divisor of p, say p = dt, then p | d or p | t. Show that this...

Hi there, I am currently learning about the quantum hall effect and am a bit confused about the edge states picture and how this fits in with the rest of the theory. In most books/review texts the theory is dicussed from the point of view of an infinite 2D system the magneteic field collapses...

Prove that the square of an odd integer is always of the 8k + 1, where k is an integer. Any help would be appreciated.

ok, a/b c/d a,b,c,d are all integers b and d are > 0 find a number inbetween a/b and b/d using a,b,c,d that is an irrational number. thanks :!)

Let SL(2,Z) be the set of 2x2 matrices with integer coefficients. I know that SL(2,Z) is generated by S and T, where S= (0 -1 1 0) and T= (1 1 0 1). But how can I show that everyone element of G (the group generated by S and T) is in SL(2,Z)? Also, let...

How is this problem solved using the Limit Sum Integer method? \int_{2}^{10} x^6 \; dx

I am a visitor of this beautiful site, my name is Angelo Spina, I would like to resolve the three following problems, in fact after many attempts I have not succeeded in it, for this reason I kindly ask you to give me a help. PROBLEM 1. If the equation y² + a p² = 2 x² (where a is a...

This one is just for fun, I do not have the answer myself. I was reminded of it by BicycleTree's procedure. The goal is to get each integer as the result of using any of the four operations, and exponentiation, operating on four fours. For instance: 1 = 4 - 4 + 4/4 2 = 4/4 + 4/4 3 = (4 + 4...

Two conjectures (or are they?): 1. The order of an integer 'a' modulo P^m = P^(m-1)*(Order of a mod P); where P is an odd prime . 2. If a, m, and n are elements of Z and (a,mn) = 1, then Order of a mod mn = QR/(Q,R); where Q = Order of a mod m and R = Order of a mod n and (Q,R) is the...

Rv=...

I understand that harmonics are integer multiples of a fundamental frequency. Also, that the relative strengths of the harmonics are what make the same note on different instruments sound different. Why are these other frequencies made? How many integer multiples are there? Why do our...

Hi everyone, This is my first post here :smile: Anyway I have problems solving this question wonder anyone could help give me some clues as to how to go about it. Here goes: The positive integers are bracketed as follows, (1), (2,3), (4,5,6,7), (8,9,10,11,12,13,14,15), ...

Hey everyone, I came across this problem recently and I'm trying to find an answer for it to satisfy my curiosity (that and it's easy to understand but hard to actually solve, so tantalizing!). Can anyone give me a nudge in the right direction? Find all ordered paris that are integer...

fi have no idea what to do and i tried posting it on another forum and nobody replied so please help me! thank you so much! find a positive integer n so that 40n is a fifth power (of an integer) 500n is a sixth power, and 200n is a seventh power, or explain why it is impossible to do so...