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. C

    Solving 2^k ≡ n mod p with Modular Arithmetic

    I'm trying to write a program which finds a solution to 2^k\equiv n\pmod p where p is an odd prime. At the moment I'm using a program like this: power = 2; exp = 1; while (power != n) { power = (2 * power) % p; // actually coded as an addition and conditional subtract if (power == 1)...
  2. K

    How to find limit of arithmetic series?

    Find the limit of the following series: lim (n-->infinity) 1 + 3 + 5 + 7 + ... (2n-1) / (n+1) - [(2n+1)/2] 3. From what I kno this is an arithmetic series, meaning I must use that arithmetic series formula. so its (first term + last term / 2 times the number of terms) n^2.. now...
  3. C

    Modular Arithmetic: Solve (a + b)^5 in Z_5

    Homework Statement Compute: (a + b)^5 in Z_5 (Z mod 5). Homework Equations The end result is apparently: (a^5 + b^5) Intuition would tell me to exploit the properties of arithmetic in Z_n, however I don't see how I can reconcile this solution with just a normal expansion of (a+b)^5 (which...
  4. N

    Arithmetic Overflow: 8-Bit 2's Compl & Estimation of Overflows

    Perform the following operations, representing the decimal numbers in 8-bit two’s complement code. Analyze whether the operations produce arithmetic overflow. Explain how you have estimated the overflows. 20 – 5; 127 –126; 127 – 128; -20 – 111; -20 – (+111); - 43 - 120; -127 – 2; - 126 –...
  5. W

    Inequalities of Arithmetic Series and Integrals

    show that 1/2+1/3+...1/n < \int dx/x < 1+1/2+1/3+...1/(n-1) inside the integral is from 1 to n. thx
  6. G

    Improve Your Arithmetic Accuracy with These Helpful Tips

    I need help making my basic arithmetic more accurate. [eg. 2*2=4] If anyone has any suggestions they are greatly appreciated. The Attempt at a Solution I tried some online games but they don't help very much. Is it really just practice practice practice?
  7. S

    Help with arithmetic in calc class please

    Given the approximate values: ln(2)=0.7 and ln(10)=2.3 Use these approximations and an indirect argument using only arithmetic to explain how many decimal digits to expect in the number 2^40 and how do you know your correct? Well i know that we'll know if we are correct based on the decimal...
  8. A

    Verilog arithmetic shift implementation.

    Here's my verilog code first of all module arithmetic_shift(input_num, op, shift_num, result); input [7:0] input_num; input [2:0] shift_num; input op; output reg [7:0] result; always @ (*) case(op) 0 : result = input_num <<< shift_num; 1 : result = input_num...
  9. S

    Solve M(x,y) from N(x,y) and Equation Provided

    Homework Statement is it possible to find M(x,y) if I know N(x,y) and the equation i need to solve is N(x,y)^M(x,y) - M(x,y)*e^N(x,y) = 0? both are linear functions thanks, this is part of a longer differential equation and the above equations is what I end up with. Just need some input...
  10. R

    Solving for Levels in a Binary Lattice - Understanding Arithmetic Series

    Hi I am currently working through the following issue: I am trying to read an list of values which contains the data points for a binomial lattice. If I have a list of N values that describes a binary tree, and I want to find out how many levels deep L the tree is, I can easily do it via the...
  11. R

    Can Arithmetic Progressions Form Infinite Relatively Prime Subsequences?

    a question came up "show that the arithmetic progression ax+b contains an infinite subsequence (not necessarily a progression), every two of whose elements are relatively prime." i have a hunch that the chinese remainder theorem has something to do with this, but I'm not sure how. any...
  12. P

    Fuzzy Arithmetic: Learn Basics & Solve Doubts

    fuzzy arithmetic... hey, I'm a newbie in this field...just know how to add, subtract, multiply, and divide fuzzy numbers... but want to learn a bit more...could u give me some gud links to some sites tht explain fuzzy numbers, etc... all i get on the net is going over my head...some simple...
  13. cepheid

    Units Digit of n: Is it Greater than 4?

    n = (28)^3 which is greater: the units digit of n OR 4? How does one go about *computing* the units digit of n?
  14. A

    Using calculus in simple arithmetic

    I've learned from early years in college. Using calculus, 1 + 1 is not really 2( in terms of accuracy)! but rounding it to the nearest integer is 2. Can someone comment on this? if it is true is there any way we can we can add 1 and 1 to an exact 2, (of course not by arithmetic) in terms of...
  15. M

    Why is the LCD of 5/2x and 7/5x3y 10x^2y and not 10x3y?

    Homework Statement LCD of 5/2x and 7/5x3yHomework Equations Lowest common denominator is also lowest common multiple: (2)(x) (5)(x)(3)(y) = (10)(x)(3)(y) I figured, the lowest common multiple of 2x and 5x3y is 10x3y. For some reason, my book shows the answer as 10x^2(y)! The Attempt at a...
  16. K

    What is the solution space for the equation 2^x - 5^y = 3 in modular arithmetic?

    Problem Determine all possible non negative integer pairs (x, y) satisfying this equation: 2^x – 5^y = 3 My Attempt: If x =0, then 5^y = -2, which is a contradiction. If x =1, then 5^y =-1, which is a contradiction. If x = 2, then 5^y = 1, so that y = 0 If x>=3, then we...
  17. C

    Fun with counting and modular arithmetic

    So today I was doing a problem out of my book for practice, and I came across some interesting results. Show that among any group of five (not necessarily consecutive) integers, there are two with the same remainder when divided by 4. a set of consecutive integers 1 mod 4 = 1 2 mod 4...
  18. P

    Sequences Series geometric series or an arithmetic series?

    This is the sequence: 1, 2, 5, 14, 41, 122 1. Is this a geometric series or an arithmetic series? 2. I know the formula is a sub n=[3^(n-1)+1]/2, but how do you get that from a sub n=a sub 1 * r^(n-1), which is the geometric formula for series.
  19. T

    Learn Binary Arithmetic: Two's Compliment & Multiplication

    I was wondering if anyone could suggest a resource to help me understand binary math better. Specifically I am having trouble two's compliment problems and binary multiplication. An example of where my thought process is getting confused: 1110 * 010 The answer given for this example...
  20. S

    Are There Simplification Rules for Modulo 1 Arithmetic?

    I was wondering whether there are any simplification/rules when doing modulo 1 arithmetic. For example: <a+b>*<c+d> = ? or <a+b>^2=? Here, <> is the fractional part, i.e <4.2> = 0.2 There is plenty I could find on mod N arithmetic with n>1 but nothing on mod 1. thanks for any tips...
  21. B

    Need help designing a Arithmetic Bit Slice Unit

    Need help designing a Arithmetic Bit Slice Unit... Homework Statement I need to design a Arithmetic Bit Slice unit built upon a full adder that performs the following operations on two bit A and B and carry in Cin. A + B A-B A+1 A-1 B+1 B-1 B A 0...
  22. C

    Why is the transition from multiplication tables to algorithms flawed?

    The problems with mathematics education cannot be fixed until the general public stops using these terms synonymously. Today the news (Good Morning America - ABC) reported an autistic savant who, although he is mentally disabled in many ways, could "solve complex mathematics". I was very...
  23. C

    Finding the Smallest Positive Term in an Arithmetic Series (C1 Level)

    Please could someone tell me the way to find the smallest positive term of an arithmetic series (C1 level) as I cannot find a formula anywhere. Thank you. Cathy
  24. mbrmbrg

    A Different Sort of Arithmetic

    There's construction going on in my university, and I found some fascinating figures written on one of the walls (presumably by the construction workers). It looked like someone had gone to a lot of trouble to prove that 7*13=28. Actually, assuming you can play mix 'n' match with units and tens...
  25. C

    Arithmetic Series help (AS Level)

    I'm totally stuck on the following question and so I'd very very grateful if someone could please tell me how to work it out. The first three terms of an arithmetic series are (12-P), 2P and (4P-5) respectively, where P is a constant. (a) Find the value of P. (b) Show that the sixth...
  26. M

    Java Transforming Infix to Postfix in Java: Solving Arithmetic Expressions with RPN

    I am creating a class that will transform a basic arithmetic expression from infix to postfix (Reverse Polish Notation (RPN)). Then after then, it will evaluate the postfix expression and give the answer. I have having a little trouble with the operators (+,-,/,0*, and %). Like, I have to...
  27. M

    Help Needed: Geometric Progression & Arithmetic Sums

    Hello everyone I'm studying for my next exam and I screwed up on the geometric progressions and arthm and they are the easiest of them all but I don't know what I'm doing wrong. The first problem on the exam said: Suppose that an arithmetic series has 202 terms. If the first term is 4PI and...
  28. JasonJo

    Bread Loaf Size Changes with Wheat Price- Trevisio Arithmetic

    When a bushel of wheat is worth 9 lire, the bakers make a loaf of bread weighing 6 ounces, when a bushel of wheat is worth 11 lire, how big is a loaf of bread? (the price of a loaf is constant) from Trevisio Arithmetic here is how i approached it, tell me if I'm wrong: let there be n...
  29. S

    Question on theorem of arithmetic euclid's algorithm

    http://img143.imageshack.us/img143/7461/divsuu6.jpg i know this question has to do with theorem of arithmetic and euclidean algorithm, but i don't even know where to start. help pls! thank you!
  30. murshid_islam

    Mastering Modular Arithmetic: Proving a2 ≡ 0 (mod n) with Expert Tips

    hi, i have started "self-studying" number theory. and since i am quite new to number theory and modular arithmetic, i need some help. how can i prove that if a2 ≡ 0 (mod n), then a ≡ 0 (mod n). thanks in advance to anybody who can help.
  31. J

    Finding the Number of Terms and Common Difference in a Finite Series

    I'm in Algebra 2, 8th grade. This question is driving me nuts! My book and notes do not help at all. The sum of a series is 2125. The first term is 43 and the last term is 127. How many terms are there, and what is the common difference? I have no idea how to find the terms, because all of...
  32. F

    Question on complex arithmetic

    Hey, I'm working on a program but I get errors when I do my function and evaluate it with x (being a complex number) lets say x = 2 + 3i and my function is f(x) = (x - 3)(x - 3)(x - 3) how would I get f(x)?
  33. K

    Are the Laws of Arithmetic Empirically Derivable?

    One stone plus 5 stones equals 6 stones. Is that a unique property of our universe, or it is conceivable that in a different universe with a different set of physical laws, arithmetic is impossible?
  34. D

    Does Erdos' Unresolved Conjecture Involve n-term Arithmetic Progressions?

    MATHWORLD: "Erdos offered a prize for a proof of the proposition that 'If the sum of reciprocals of a set of integers diverges, then that set contains arbitrarily long arithmetic progressions.' This conjecture is still open (unsolved), even for 3-term arithmetic progressions. " What's an...
  35. K

    Help! Prove Sum of Arithmetic Sequence's First 13 Elements = 65

    i need help- arithmetic sequences There many arithmetic sequences which seventh term equals 5. prove all of them have the same sum of their first 13 elemnets. find the sum i found the sum was 65 but i don't know how to prove it.
  36. H

    Mathematica Mod. arithmetic in mathematica

    Hello, I'm not very experienced with mathematica, and I have some problems in making an equation like this, Find x such that 11x = 1 (mod 360) and x < 360. Any ideas on how to input this into mathematica? Thanks,
  37. A

    Solve Arithmetic Series: Find Sum & Term - Check Answers!

    OK, these questions are supposed to be really easy, but I keep geting the wrong answer and I don't understand why, could someone pleas look at my work and tell me what I am doing wrong? Find the indicated sum of each arithmetic series S15 for 4 + 11 + 18 + ... Sn= n/2 [ 2a + ( n - 1 ) d...
  38. R

    Factors of triangular numbers forming arithmetic series

    For every pair (a,b) of factors that equal the trangular number m(m+1)/2 there are two distinct sets of pairs (c,d) that form a determinant equal to 2m+1 such that the products (a+cn)*(b+dn) = a triangular number for all n. Is this a previously known fact and how can it be prooved?
  39. B

    Solve Index Arithmetic Problem: ax^4≡2 (mod 13)

    How would i go about solving the problem of for which values of a is the congruence ax^4≡2(mod 13) solvable? I think it might have something to do with power residues but I'm not sure. Thanks
  40. Gamma

    Arithmetic Sequences: Examples & Solutions for 35th, 57th Terms

    1. Give an example of an arithmetic sequence such that the 35th term is 4,207? I used the general form of an arithmetic seq. an = a1 + (n-1)d and found that, a1 = 25, and d = 123 Does this look ok? I had to use some trial and error since we have two unknowns.2. What is the 57th smallest whole...
  41. M

    Is arithmetic still true in a gravitational field

    It is well-known that Euclidean geometry does not hold in a gravitational field. Because of equivalence, an entity in circular motion is effectively the same as an entity in a gravitational field. Now because length shortens in the direction of motion in accordance with special relativity...
  42. D

    Find Sum of Arithmetic Series & Sum of Numbers Divisible by 8

    8a) The first and third terms of an arithmetic series are 3 and 27 respectively. i) find the common difference ii) find the sum of the first 11 terms of the series b) find the sum of the inteers between 50 and 150 which are divisible by 8. I have already done part a) and found the common...
  43. N

    How Many Ways Can a Number Be Represented as an Arithmetic Series Sum?

    I have been asked to write up a 20 page report on the following... For example 2 + 3 + 4 = 9 or 7 + 8 + 9 +10 = 34 Investigate this theme? (Hints from my teacher how many ways can a number be thus obtained? Could you specify which numbers can be done in just one way, two ways, etc. Use the...
  44. P

    Array Arithmetic in C: Incrementing Integers in an Array

    int f[5]; Is it possible to do f[i]+=1; inside a valid for loop? If not than how can I increment integers stored in an arrary for each i in C? Thanks
  45. I

    What is the theorem about modulos and relatively prime numbers?

    Is it possible to manipulate and substitute modulos like so a^5 = a (mod 5) a^3 = a (mod 3) a^15 = a (mod 15) By substituting the first into the second?
  46. R

    How can complex calculations be done in seconds solely using mental arithmetic?

    I once saw a programme not so long ago, showing a young man who was calculating something like 56^6 in a matter of seconds. And also working out square roots of numbers in seconds all entirely in the head. Could someone tell me how calculations like that can be performed so quickly ? (I...
  47. Y

    Proving the Sum of an Arithmetic Series Formula

    i am given an formula Sn= n/2[2a+(n-1)d] and i am told to verify the formula represents the sum of n terms of an arithmetic series. How do i verify this?
  48. B

    Modular Arithmetic Word Problems

    Hi, I'm currently trying to do some modular arithmetic questions but I don't really know where to start, I don't have much in the way of examples, only a list of theorems. I'm no genius so theorem's by themselves are not enough to enable me to apply them so I've been stuck on some questions. Can...
  49. B

    Modular arithmetic + some other stuff on numbers

    Hi, I've just begun studying modular arithmetic and as yet, I haven't got a reference text to work from so I'm hoping that someone can help me out with the following questions. Q. Calculate 7^2(mod 13), 7^4(mod 13), 7^8(mod 13) and 7^9(mod 13). I can't think of a way to do this without...
  50. G

    Modulo Arithmetic: Division Defined?

    Hey, umm... I can't find an answer for this anywhere. if we have a group \mathbb{Z}/p\mathbb{Z} (for sufficient p) under multiplication modulo p, is divsion defined \frac{a}{b} = ab^{-1} ie in \mathbb{Z}/5\mathbb{Z} = \{1,2,3,4\}; would \frac{3}{2} be (3)(2^{-1}) \equiv (3)(3) \equiv 4...
Back
Top