Integer Definition and 606 Threads

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...

I have 2 questions. 1)what is the remainder with 100! is divided by 103? explain your answer 2)a = 238000 = 2^4 x 5^3 x 7 x 17 and b=299880 = 2^3 x 3^2 x 5 7^2 17. Is there an integer so that a divides b^n? if so what is the smallest possibility for n? the first one i have no...

Hello all, I've been asked for a graduate level course to do a proof using induction that shows that nCr always turns out to be an integer. I thought that I might use Pascal's triangle somehow and the fact that nCr is equal to n! / r!(n-r)! (I saw a brief explanation of this while doing a web...

I have my question and my problem in the attachment that followed.

Hai COuld you please help the formula as I am not able to identify the question below: Question: For a Traingle with a perimeter of 30cm, what is the integer value of the longest possible side ? REgards aprao

Can anybody explain what appear to be discrepancies in the way the following expressions are interpreted by Hugs (Haskell98 mode) ? Main> div -6 4 ERROR - Cannot infer instance *** Instance : Num (b -> a -> a -> a) *** Expression : div - fromInt 6 4 Main> div (-6) 4 -2 Main> -6...

I just completed Trigonometry and College Algebra, and I'm heading into Calculus, so i thought i would get a head start on the material. So right now I'm working out of an old calculus book i got at the library. Then i came across this problem: A dial-direct long distance call between two...

for n- fixed integer prove that phi(x)=n has a finite number of solutions I looked at 2 cases when x is even and when x is odd 1) if x is even then phi(2x)>phi(x) and I showed why it has a finite number of solutions 2) I'm not sure how to show for the case when x is odd.. any ideas? thanks :)

The terms of this series are reciprocals of positive integers whose only prime factors are 2s and 3s: 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+... Show that this series converges and find its sum. this is my first time writing here. i hope someone can help me with this question.

How many pairs of positive integer a, b are such that a^2 + b^2 = 121?

I'm not a very logical person, and I would hardly consider math a strength so, I'm stuck with these proofs: 1. Prove that every positive integer, ending in 5 creates a number that when squared, ends in 25 2. Prove that if n is an even positive integer, then n^3 - 4n is always divisible by...

I am having trouble with this one... Prove that any positive integer whose ALL digits are 1s (except 1) is not a perfect square.

I have an integer A and a possitive odd integer B, can you tell me how to find a nonnegative integer C such that C<2^A and 1+BC=0(mod 2^A) ? ?

The Q is: show that the number of partitions of n within Z+ where no summand is divisible by 4 equals the number of partitions of n where no even summand is repeated Here is what I got so far Let the partition where no summand is divisible by 4 be P1(x) Let the partition where no even...