Arithmetic Definition and 479 Threads

Homework Statement A particle moves in a straight line away from a fixed point O in the line, such that when its distance from O is x its speed v is given by v=k/x , for some constant k. (a) show that the particle has a retardation which is inversely proportional to x3 The answer is...

Rather than arithmetic ("plus or minus") uncertainties, are there classical (not of Heisenberg uncertainty principle) measurements whose uncertainties otherwise appear as geometric ("times or divided by")?

This program has been assigned in my intro to programming course, which assumes no previous knowledge of programming. Up to this point we've only been required to write functions that accomplish specific tasks within a program. This is the first time we've been asked to design and write a full...

I'm trying to prove something in modular arithmetic that I came upon across my studies in comp sci. Consider a set of natural numbers {n_{1},n_{2},n_{3},...n_{k}} Consider two more natural numbers m and p such that (\sum^{k}_{i=1}n_{i} ) \ mod \ m = p Now prove that ((((n_{1} \...

I have to do the following using these axioms PA1-7, the others below it are previously proved results I can use too. [Sa] means the successor of a. Base Case: y = S0 x.S0 = S0 → x.0 + x = S0 → 0 + x = S0 → x = S0 & y=S0 Now the induction step is usually y=a to y=Sa, however this does...

if {x1 , x2 , ...xi} and {y1,y2,...yi} are finite sets. are two sets of real numbers. Then sum Ʃ xixj +yiyj must be maximum, and i≠j so is there some general condition to solve this problem?

Fairly recently someone started a topic here regarding the conjecture of Erdos about arithmetic progressions, namely that if A is a subset of the natural numbers and the sum of the reciprocals of elements of A diverges, then A contains arbitrarily long arithmetic progressions. I'm looking for...

I read this through wikipedia and some other sources and find it to be unsolved. Erdos offer a prize of $5000 to prove it. A mathematician at UW has looked at it and verify them to be correct. However, i still have some doubt about it because the proof i give is pretty simple. Can anyone take a...

Homework Statement Wrote a code using Fortran 95 to solve for an advection-dispersion equation but at the spatial steps specified at dx = 20 m over a total length, L of 20000 m, I keep getting an arithmetic overflow error. I have run this same program at smaller spatial intervals (dx =...

My discrete mathematics book gives the following definition for the pigeonhole principle: If m objects are distributed into k containers where m > k, then one container must have more than \lfloor\frac{m-1}{k}\rfloor objects. It then states as a corollary that the arithmetic mean of a set...

Homework Statement Posted this thread earlier but had mis read the given answer. please disregard older thread as I don't know how to delete it! Write down the condition for the numbers p, q, r to form an arithmetic sequence & geometric progression. Homework Equations \ a_n =...

Homework Statement Write down the condition for the numbers p, q, r to form an arithmetic sequence. Homework Equations The Attempt at a Solution Have no idea, but I looked at the answer and they have assigned each letter with a given value (number). How is this possible?

I've recently been into mental math and I'm learning how to do arithmetic mentally without the need of calculators or computers, I know that abacus could be a great help for me now, so I bought one. I've figured out how to add and subtract numbers, I also have figured out how to do...

Homework Statement Prove that for any n \in \mathbb{N} and x \in \mathbb{R}, we have \sum_{k = 0}^{n} {\cos{(kx)}} = \frac{1}{2}+ \frac{\cos{(nx)} - \cos{[(n+1)x]}}{2 - 2\cos {x}} Homework Equations None I can think of. The Attempt at a Solution Try induction. The result holds if n = 0...

Homework Statement V0=4 V_{n+1}=\sqrt{V_{n}^{2}+2n+3} Homework Equations Show that Un is an arithmetic sequence. The Attempt at a Solution I counted Vn and i found that it equals: V_{n}=\sqrt{(Vn+2)^{2}+2} what is there to do after this?

Our 8th grade math counts team met today and I didnt know how to do this problem: The first three terms of an arithmetic sequence are p, 2p+6, and 5p-12. What is the 4th term of this sequence? Please explain how to do this. Arigato!

I think a best informal way to state the theorem is Hardy's: every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes But clearly, this statement does not reveal the structure of the statement in the formal...

So, I'm trying to learn prolog, and since it's used a lot in the AI community, I thought I would try my hand at implementing a few of the simple "wumpus world" rules. The rule for a "pit" existing at location (2,2) means that a breeze is felt at locations (1,2), (2,1), (2,3), and (3,2). So...

what is 3(or i, where i=1,2,3,4...∞) digit arithmetic? is it just working with 3 decimals or 3 significant figures? or is it base 3 arithmetic?

Homework Statement Two consecutive numbers from 1,2,3...n are removed A.M of remaining numbers is 105/4. Find n and those numbers removed .Homework Equations Answer n = 50 those numbers are 7 and 8 The Attempt at a Solution I solved this question like a few weeks ago but now it escaped my...

Homework Statement If x ε R, the numbers 51+x+51-x, a/2, 25x +25-x form an AP, then 'a' must lie in the interval:- a)[1,5) b)[2,5] c)[5,12] d)[12,∞) Homework Equations Not required The Attempt at a Solution I substituted y=5x. The terms are in AP, so the common difference is...

Hello, I'm new to modular arithmetic, but I was wondering - Given that b = R mod(n) where b,R, and n are all integers Is it plausible to consider G(x) = R(x) mod(f(x)) with G,R,f all functions of x? Has this been done or does this not even make sense? If its been done, what is it...

Hello, I tried to figure out what is the maximum count of arithmetic operation (*,:,+,-) need for gauss elimination and gauss-jordan elimination, but can not get it right. what I get from wikipedia is but I don't understand how to get to this result. Thanks for any help.

Homework Statement When x=! -1, y=! -1, x=! -y then x and y are two numbers so that 1/(x+1) + 1/(x+y) + 1/(y+1)... is an arithmetic serie. Show that then also x2 + 1 + y2... must be an arithmetic serie. The Attempt at a Solution I tried to find the differentials between each number in...

Homework Statement I have already converted the following numbers 15,765 and -8,773 into 9's complement form. Which gave me the result: 9's Complement of 15,765 = 99,999-84,234 = 84,234 9's Complement of -8,773 = 99,999-(-8,773) = 108,772 Now that I converted the following 5 digit numbers...

PROVE mean (X bar) of a continuous distribution is given by: ∫x.f(x)dx {'a' is the lower limit of integration and 'b' is the upper limit}

Homework Statement Let p be a prime number. Prove: (a+b)^p modp = [(a^p modp) + (b^p modp)]modp Homework Equations modular arithmetic. The Attempt at a Solution I honestly haven't the slightest clue. Would induction be my best bet here? If so, when I suppose the...

Homework Statement Suppose a, b, n are integers with n >/= 2 Prove that: (a + b) mod n = ((a mod n) + (b mod n)) mod n Homework Equations Modular arithmetic rules. The Attempt at a Solution r1 = a(modn) => a = q1n + r1 r2 = bmodn => b = q2n + r2 r1 + r2 = a -...

Why is it that when using 2's complement, the result of arithmetic operations differ by two? 11011001 (-39) + 11100111 (-25) = 11000000 (which is -62 in 2's complement, even though it's supposed to be -64) 00110011 (51) + 11101110 (-16) = 00100001 (33, but it's supposed to be 35)

Homework Statement I am asked to prove that (\sim x)\vee z = \sim(x\vee y)\vee\sim(y\vee\sim z)\vee\sim(x\vee\sim y)\vee\sim(\sim y\vee\sim z). I've tried using all combinations of DeMoran's rule, the distributive rule to get the y terms together, and the absorption rule to get rid of the...

Homework Statement Let n be a fixed positive integer greater than 1. If a (mod n) = a' and b (mod n) = b', prove that (a+b) (mod n) = (a'+b') (mod n) and that (ab) (mod n) = (a'b') (mod n) Homework Equations When a = qn + r a mod n = r The Attempt at a Solution (a'+b') (mod n) = (a...

two questions. I know I'm doing the work right, but I can't get my answers to match and they are pretty close. I think it's just some arithmetic errors. Help? I've been trying to solve my mistakes forever. I can't find them! Homework Statement Use the parametric equation of an ellipse x =...

1. Homework Statement . 1. Let a and b be constant integers with a \not = 0, and let the mapping f : Z \rightarrow Z be defined by F(x) = ax + b. Determine all values of a such that f is a bijection. Prove that the aforementioned values are the only possible values resulting in a bijection. The...

If p is a prime and a an integer coprime with p, why is a^{\frac{p-1}{2}}\equiv -1 mod p ?

As stated in the title, I am trying to prove a statement by minimum counterexample involving modular arithmetic. My problem is producing the contradiction, but I feel so close! (The contradiction is p^m | (1 + p)^{p^{m - 1}} - 1) Homework Statement Let p be an odd prime and let n be a...

Hi, I am trying to learn maths at home and was wondering if anyone knew of any series(or group of books that you would recommend) of books with the structure: learn arithmetic practice arithmetic learn algebra practice algebra and so on up until calculus or higher I would prefer if the...

Let (N, s(n), 0) be a Peano space. That is, N=\{1,2,3,\dots \} is a set in which http://en.wikipedia.org/wiki/Peano_arithmetic" can be used. We can then define: 0=\varnothing, 1=\{0\}, 2=\{0,1\},\dots \implies n=\{0,1,2,\dots ,n-2,n-1\} s(a)=a\cup \{a\}\implies s(a)=a+1 From here we...

Homework Statement The sum of the first 8 terms of an AP is 56, and the 6th term is 4 times the sum of the 2nd and the 3rd. Find the first term and the common difference Homework Equations The Attempt at a Solution 8th term = 56 6th term = 4x2nd+3rd

Hello, I'm wondering if this is true, or if anyone has seen this before: Let q, t be coprime integers. Then there exist infinitely many primes r such that 1. q is primitive root modulo r and 2. r = q + kt, for some k > 0.If we take away 1, this becomes Dirichlet's Thm...

Homework Statement Just a quick question I was looking to have cross checked… Q. Find un, the nth term of sequence -5, 0, 5, 10,… Homework Equations un = a + (n-1)d The Attempt at a Solution -5 + (n-1)5 -5 + 5n - 5 5n-10 The answer in the book...

I've recently started development on a continued fraction based exact arithmetic computational package. This is work based on Bill Gosper's HACMEM algorithm and Peter Potts' Mobius transforms with significant modifications. These algorithms have some remarkable properties and can be made much...

Why doesn't the integration of the general term of an A.P. give its sum? Integration sums up finctions, so if I integrate the general term function of an A.P., I should get its sum. Like 2,4,6,8,... T=2+(n-1)2=2n \int T dn=n^2 ..(1)...

Homework Statement A woman started a business with a workforce of 50 people. Every two weeks the number of people in the workforce increased by 3 people. How many people were there in the workforce after 26 weeks? Each member of the workforce earned $600 per week. What was the total wage bill...

Hello, I have been searching and can't seem to find anything on the topic of integrating modular arithmetic functions. So far I have created an equation for a function in the form of f(x)=mod(x,a): \int mod (x,a) dx=\frac{a(x-mod (x,a))+mod (x,a)^2}{2}+c But, now I am investigating how to...

Homework Statement Find dy/dx for the following function: y = (11-cos(x))/(2+cos(x)) Homework Equations Quotient Rule: y'= ((g(x))(f'(x)) - (f(x))(g'(x)))/ (g(x)^2) The Attempt at a Solution I used the quotient rule to come up with this: y'= ((2+cos(x))(sin(x)) -...

Given N= 1.2.3 + 2.3.4 + ... + n(n+1)(n+2), prove that 4N + 1 is a square (n is a positive integer)

In some exercises I've stumbled upon a function which is denoted \gamma_{m}(n) with m,n natural. I've no idea what is the definition of the function and could not infer from the exercises. Searching google yielded nothing, as it kept suggesting me the OTHER Gamma function. Can anyone here help...

The prime number theorem describes the distribution of the prime numbers, in a sense. Are there other prime number theorems corresponding the asymptotic distributions of primes in other arithmetic progressions containing infinitely many primes? I was just wondering.

Greetings. This is my first post, please be gentle! I am a music theorist who uses a lot of math in my investigations of music. I am writing a paper about transposition and multiplication operations by 1, 5, 7 and 11 which have very interesting properties in music. The reason, of course, is...

Homework Statement Problem 1: Two Arithmetic Sequences are given. a_n = 200,196,192,188,184... [ltaex]b_n = 100,103,106,109,112...[/itex] For integers l,m, find the number of pairs consisting of (l,m) which satifies condition a_l = b_m Problem 2: Three terms, sin(x)...