What is Arithmetic: Definition and 476 Discussions

Arithmetic (from the Greek ἀριθμός arithmos, 'number' and τική [τέχνη], tiké [téchne], 'art' or 'craft') is a branch of mathematics that consists of the study of numbers, especially concerning the properties of the traditional operations on them—addition, subtraction, multiplication, division, exponentiation and extraction of roots. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory, and are sometimes still used to refer to a wider part of number theory.

View More On Wikipedia.org
Recent contents Top users
  1. D

    Arithmetic Sequence for homework,im also new to this website

    Homework Statement a, b and c are consecutive numbers in a geometric sequence, where a+b ≠ 0 and b+c ≠ 0 * "/" means divide * Show that 2ab/a+b, b and 2bc/b+c are consecutive terms in an arithmetic sequence The Attempt at a Solution i know this has something to do with it...
  2. L

    Vectors with a dose of arithmetic :3

    Homework Statement Two velocities acting at a particular point are such that: The sum of their respective magnitudes is 15m/s The product of their respective magnitudes are 56m2/s2 The resultant is 13m/s. Find the two velocities and the angle between them. Homework Equations R^2 = P^2 + Q^2...
  3. D

    MHB Error in fixed point arithmetic library

    I found an issue with the fixed point library, and Heiko Oberdiek found the offending code and submitted a correction to fix the problem in the fixed point library. The details can be found here. At present, you can issue the command below to over come the problem. Eventually someone will...
  4. C

    Arithmetic Question Involving Quantum Physics

    Homework Statement Two adjacent allowed energies of an electron in a one-dimensional box are 2.0 eV and 4.5 eV. What is the length of the box? Homework Equations E_n=\frac{h^2n^2}{8mL^2} The Attempt at a Solution My question is, since E_n and n^2 are both on separate sides of the equation...
  5. U

    Arithmetic Progression problem

    Homework Statement Let a1,a2,a3...,a4001 are in A.P. such that \dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+.......\dfrac{1}{a_{4000}a_{4001}} = 10 and a2+a4000=50. Then |a1-a4001| The Attempt at a Solution \dfrac{1}{a_2} \left( \dfrac{1}{a_1} + \dfrac{1}{a_3} \right) + \dfrac{1}{a_4}...
  6. C

    MHB Proving Modular Arithmetic for x^2 = 0 or 1 (mod 4)

    Hello, new to the forums here. I need to prove that for all integers x, x^2 = 0(mod4) or x^2 = 1(mod4). I started out by making a table of different cases. case 1: y=0 ->0mod4 case 2: y=1 ->1mod4 case 3: y=2 ->0mod4 ... case odd: y=2n ->0mod4 case even: y=2n+1 ->1mod4 From here, I'm not...
  7. J

    Gauss's Trick - Arithmetic Sums

    I can't grasp the underlying process on how this is working. n/2(f+l) = algorithm sum of all integers n= number of all integers f= first integer l= last integer Example: 1, 2, 3, 4 4/2(1+4) 2(5) = 10 I know how to do it, but I don't really understand how to actually do it. Am I...
  8. C

    Proof about arithmetic progressions

    Homework Statement Prove that there exist arbitrarily long arithmetic progressions formed of different positive integers such that every 2 terms of these progressions are relatively prime. The Attempt at a Solution First i started to think about the odd integers like 2x+1 and how...
  9. z.js

    Arithmetic Progression Problem

    Homework Statement If the sum of the first 7 terms of an arithmetic progression is 28 and the sum of the first 15 terms is 90, find the sum of n terms.:eek: Homework Equations Sn = 0.5n[2a+(n-1)d] a is the first term and d is the common difference. n is the number of terms. nth term =...
  10. S

    Now, what does that give you in this problem?

    Homework Statement For any integers a and b and any positive integers k and j, if ##a \equiv 2-b \pmod{k}## and ##j \mid k##, then ##a^2 + 4b - b^2 \equiv 4 \pmod{j}## Homework Equations ##x \equiv y\pmod{q}## then q|x-y The Attempt at a Solution At first I thought this would...
  11. R

    Is Peano Arithmetic Essential for Understanding the Logic-Math Connection?

    It seems that learning PA is necessary if you want to understand the relationship between logic and math. Should I track down this book at the library, a chore which will take up an hour of my precious time The principles of arithmetic, presented by a new method" in Jean van Heijenoort...
  12. MarkFL

    MHB Ernesto's Question: Proving Harmonic & Arithmetic Progressions

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  13. L

    Middle Terms in an Arithmetic Series

    Homework Statement An arithmetic series consists of 2n terms. Which are the two middle terms of the series? If the first term is a and the last term is b, find the middle terms and the sum of the series. Homework Equations The Attempt at a Solution I'm having problems finding out...
  14. anemone

    MHB Arithmetic Progression Problem

    Find three irreducible fractions $\dfrac{a}{d}$, $\dfrac{b}{d}$ and $\dfrac{c}{d}$ that form an arithmetic progression, if $\dfrac{b}{a}=\dfrac{1+a}{1+d}$, $\dfrac{c}{b}=\dfrac{1+b}{1+d}$.
  15. T

    Simple vector arithmetic question

    I have two vectors: a = <ax, ay, az> and c = <cx, cy, cz> which have an angle of 45 degrees between them. If I get another vector by b = c - a then shouldn't b be orthogonal to a? I'm assuming this since a + b = c
  16. Albert1

    MHB Arithmetic Sequence: Definition & Examples

  17. JJBladester

    Geometric Mean vs. Arithmetic Mean in Bandpass Filters

    Why is the geometric mean used to define the center frequency of a bandpass filter instead of the arithmetic mean? I read in this book that 1. All the lowpass elements yield LC pairs that resonate at ω = 1. 2. Any point of the lowpass response is transformed into a pair of points of the...
  18. M

    Convert this arithmetic to calculus

    a = b : this set = this many pieces a % b = c : this set % this many pieces = this many sets c * b = a : this many sets * this many pieces = this set a : c = b : this set % this many sets = this many pieces per set step 1.) a = 8 pieces step 2.) a / 4 pieces per set = 2 sets step 3.) 2...
  19. mathbalarka

    MHB Arithmetic Geometry on 2-sphere: Mordell-Weil Finiteness

    Consider a 2-sphere on the real plane equipped with the linear map from the sphere to it's equatorial 2-plane by fixing the topmost vertex of the sphere. This is now an analogue of the Riemann sphere in 3-dimensional space, hence we have the "point at infinity" in addition to the usual reals...
  20. T

    MHB Arithmetic Sequence: Find Initial Term & Sum to 243

    In arithmetic sequence we know that a_1+a_3 = 6 and 3^{a_1+a_2}=243 a) Find the initial term of the sequence b) Calculate,how much members of the sequence we have to add (a_1+a_2+...a_n) that we get the result 243? Have no idea where to start :confused:
  21. P

    MHB Arithmetic progression question

    Hey, What is the greatest number a k-term arithmetic progression starting with 1 can end in if each term is less than or equal to n? I'm looking to write this as an expression involving n and k in order to count the number of arithmetic progressions of length k with each term in $[n]$, that is...
  22. C

    Prime Factorization (Arithmetic)

    Homework Statement Assume n = p_1*p_2*p_3*...*p_r = q_1*q_2*q_3*...*q_s, where the p's and q's are primes. We can assume that none of the p's are equal to any of the q's. Why? Homework Equations The Attempt at a Solution I am completely stuck on this. My understanding of the...
  23. MarkFL

    MHB Find First Term in Arithmetic Series | Alycia's Question

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  24. C

    What are some examples of modular arithmetic proofs involving positive integers?

    Homework Statement I am required to prove/disprove the theorem: If a_1 is congruent to b_1 (mod n) and a_2 is congruent to b_2 (mod n), then (a_1)^(a_2) is congruent to (b_1)^(b_2) (mod n). Homework Equations a_1 is congruent to b_1(mod n) can also be expressed as b_1=a_1+q*n...
  25. matqkks

    MHB Modular Arithmetic: Introduction to Congruences & Interesting Applications

    What the best way to introduce congruences in a number theory course? I am looking for something which will have an impact. What are the really interesting applications of congruent mathematics?
  26. Mentallic

    Solving Modulo Arithmetic Problem with Variable Integer k

    I've stumbled across an arithmetic problem that's getting the better of me, so I need your help! I have a constant set of integers [m,n], m>0, m\neq n and a variable integer k>0. If we multiply k by successively increasing positive integers t, we will eventually get kt > m. Now, what I want...
  27. M

    Composition: Arithmetic is futile

    Please watch from 0:00 to 1:23 Goal: Complete a short essay on my greatest accomplishment achieved. I have not achieved it yet, but my greatest accomplishment will be the language of mathematics. I thought about this last night, "The difference between arithmetic in algebra &...
  28. B

    A geometric sequence within a arithmetic sequence

    the main question here is that can a sequence * arithmetic * be correct if the difference is also changing in terms of a geometric sequence ?\ now look at this sequence 0.33,0.3333,0.333333 now if we calculate the difference between the first two terms its 0.0033 between the second and...
  29. C

    Is There a Mathematical Link Between These Equations?

    I've noticed 2 x 0.2 x 0.8 happens to give the same result with 1 - (0.2^2 + 0.8^2). Can the latter be rearranged to the first? And if yes, can someone direct me to the name of the branch of math that describes this problem? It definitely reminds me of something from high school I didn't pay...
  30. karush

    MHB What is the Sum of an Arithmetic Sequence?

    I am new to this topic so... Let $S_n$ be the sum of the first $n$ terms of the arithmetic series $2+4+6+...$ this one looks simple $S_n=2+2n$ Find $S_4$ and $S_{100}$ $S_4=2+2(4)=9$ $S_100=2+2(100)=202$ is arithmetic series and arithmetic sequence the same thing?:cool:
  31. anemone

    MHB Arithmetic Progression Challenge

    Find distinct positive integers a,\;b, and c such that a+b+c,\;ab+bc+ac,\;abc forms an arithmetic progression.
  32. L

    Arithmetic mean and standard deviation

    Homework Statement Showing all your working, calculate the arithmetic mean and standard deviation of the number of days lost. Table shows man days lost to sickness.. Days lost: 1-3 4-6 7-9 10-12 13-15 Frequency 8 7 10 9 6 Homework Equations...
  33. E

    MHB How Does Modular Arithmetic Prove the Irrationality of Root 3?

    Hi everyone, I am new to the site so please let me know if I'm posting in the wrong place. I am starting to teach myself number theory and would like a bit of help with a problem. How would I go about showing "If m^2 = 0 (mod 3) then m = 0 (mod 3)"? I am then asked to deduce that root 3 is...
  34. S

    Why do we make arithmetic mistakes?

    I know the question does not strike as being specific to physics, but please, give it a look. Human brains are considered complex computing machines and are rightly so as seen by the examples around us. Why then is it that we make conscious arithmetic errors( For example: calculating...
  35. C

    Proof about arithmetic progressions

    Homework Statement Prove that there exist arbitrarily long arithmetic progressions formed of different positive integers such that every two terms of these progressions are relatively prime. The Attempt at a Solution I first thought of looking at odd numbers separated by a powers of 2 but...
  36. L

    Arithmetic mean complex numbers

    Can the arithmetic mean of a data set of complex numbers be calculated? if so, can the method be demonstrated?
  37. H

    Arithmetic progression used to determine geometric progression

    Homework Statement an arithmetic progression(a1-a9) has 9 numbers. a1 equals 1 The combination(S) of all of the numbers of the arithmetic progression is 369 a geometric progression(b1-b9) also has 9 numbers. b1 equals a1(1) b9 equals a9(unknown) find b7 Homework Equations...
  38. Lebombo

    Is this sequence arithmetic, geometric, or neither?

    Homework Statement Is the sequence \frac{1}{1}, \frac{1}{2}, \frac{1}{3} , \frac{1}{4}...\frac{1}{n} arithmetic or geometric? Homework Equations Common difference and Common ratio formulas The Attempt at a Solution I found the common difference from a_{2} - a_{1} =d_{1} and common...
  39. Monique

    How to calculate arithmetic sum of multiple strings

    I have a MySQL database and I have the problem that queries take way too much time. I want to optimize the database and one way would be to save data into a string, instead of in rows (the string would be replicates of the same condition). Each string is an interval of 4 seconds, to reduce the...
  40. Government$

    Geometric and arithmetic series

    Homework Statement If a,b,c, are at the same time fifth, seventh and thirty seventh member of arithmetic and geometric progression then a^{b-c}b^{c-a}c^{a-b} is: The Attempt at a Solution I tried solving system of equations but i have four unknown. I was able to reduce it to on unknown...
  41. B

    MHB Evaluating Arithmetic Expression

    I need help figuring out what the little 2 next to an equation means this is what my problem looks like I have the answer but I can't figure out how it was found out. (3)(-4)2 - (3)(-5) so the 2 next to the 4 in parentheses is little.
  42. MarkFL

    MHB Rudra Rath's question at Yahoo Answers involving an arithmetic series

    Here is the question: Here is a link to the question: An arithmetic progression question!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  43. MarkFL

    MHB Sundar Pangeni's question at Yahoo Answers regarding arithmetic progressions

    Here is the question: Here is a link to the question: Problem of arithmetic progression. Please help...? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  44. FeDeX_LaTeX

    Arithmetic Sequence Homework: Find the Sum

    Homework Statement This is taken from STEP I 1990, Q4. (i) The sequence a1, a2, ..., an, ... forms an arithmetic progression. Establish a formula, involving n, a1, and a2, for the sum of the first n terms. (ii) A sequence b1, b2, ..., bn, ... is called a double arithmetic progression if the...
  45. ArcanaNoir

    Arithmetic progression topology, Z not compact

    Homework Statement The Dirichlet Prime Number Theorem indicates that if a and b are relatively prime, then the arithmetic progression A_{a,b} = \{ ...,a−2b,a−b,a,a+b,a+2b,...\} contains infinitely many prime numbers. Use this result to prove that Z in the arithmetic progression topology is not...
  46. S

    MHB Logic problem with arithmetic and inequalities

    Given: 1)it is not true that : 2>0 and 2+3 =7 2)if it is not true that 2>0 then 2 is less or equal to zero 3)if 2+3 =7 ,then 3+3 =8 4) but 3+3 is not equal to 8 Then prove: 2 is less or equal to zero
  47. B

    Does modular arithmetic have different rules for different cases?

    Homework Statement I'm trying to prove the following (as part of an isomorphism problem). The problem is I don't know much about modular arithmetic, so would appreciate some help. 2((a+b)mod \ 2π) = (2a+2b)mod \ 4π. given that a,b are both nonnegative and less than 2π. Homework Equations...
  48. P

    Arithmetic and Geometric Series (tortoise and the hare)

    Homework Statement The question is attachedk Homework Equations Sn = n/2[2a+(n-1)d] Sn = (a x (1-r^n))/1-r The Attempt at a Solution I already found the general formulas: Tortoise: Sn = n/2(40) Hare: Sn = (1000 x [1-0.5^n])/0.5 And I know that there tortoise will finish the...
  49. M

    Modular Arithmetic (someone check my work please)

    Homework Statement For every x in Z and for every natural number n if: x^{2}\equiv1(mod47)\Rightarrow x^{n}\equiv1(mod47)orx^{n}\equiv46(mod47) The Attempt at a Solution Alright I said since 47 is prime and relatively prime with x then by fermat's little theorem we will get...
  50. E

    Is the gray code arithmetic code ?

    hi is the gray code arithmetic code?why? where this code used?
Back
Top