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.

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  1. S

    Arithmetic of of integrable functions

    hello all i have been trying to prove a property of integrable functions, i had a go at it don't know if it is correct, but I am wondering if there could possibly be a shorter simpler way of proving it alright here we go \int_{a}^{b} f(x)+g(x) dx= \int_{a}^{b} f(x)dx +\int_{a}^{b} g(x) dx...
  2. S

    Arithmetic of Series: Why $\sum_{k=1}^{n} k- \sum_{k=1}^{n} (k-1) \neq 1$

    hello all a simple question how come \sum_{k=1}^{n} k- \sum_{k=1}^{n} (k-1) \not= 1 even though i know if you expand it out you would get n, isn't there an arithmetic property of series that relates to this? thanxs
  3. wolram

    Arithmetic Algebraic Geometry at the University of Arizona

    http://www.arxiv.org/abs/math.NT/0505354 Authors: C. Deninger Subj-class: Number Theory; Dynamical Systems MSC-class: 11-02; 11R42; 34C25; 37C27; 53C12; 58B34 This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic...
  4. J

    Quick questions about modular arithmetic

    99999^{99} + 1 As 99999 \equiv24(mod \25) Can I say then: 99999^{99} + 1 \equiv24^{99} + 1(mod \25), or is it 99999^{99} + 1 \equiv24^{99}(mod \25) + 1, or are these two the same things?
  5. B

    Unraveling the Modular Arithmetic Puzzle

    This is another puzzle that has to do with modular arithmetic (the other one that did was Picture Puzzle). 1 1 2 1 3 2 4 1 4 5 2 3 6 1 6 4 3 9 2 8 7 5 10 What's the next row?
  6. J

    A) Is the length of the spring finite with infinitely many loops?

    Hey... I'd appreciate it if someone could verify these answers... Q1) An object is dropped from an airplane. During the first second, the object falls 4.9 m. During the 2nd second, it falls 14.7 m. During the third second, it falls 24.5 m. During the fourth second, it falls 34.3 meters. If...
  7. M

    Arithmetic progression Trouble

    The first term of an arithmetic progression is (1-x)^2 and the second term is 1+x^2 .If the sumj of the first ten terms is 310 , find the possible values of x. I have my A/S maths exam next month, but i am still having trouble with arithmetic progression. The above question is causing me some...
  8. I

    Frivolous theorem of arithmetic on Wikipedia

    [SOLVED] Frivolous theorem of arithmetic on Wikipedia http://en.wikipedia.org/wiki/Frivolous_Theorem_of_Arithmetic There's a debate on whether we should delete this theorem from Wikipedia because some consider it "useless". Should it be deleted?
  9. M

    An arithmetic & geometric progression question.

    I have an arithmetic series, with the sum of the first n terms to be 610. The 1st, 3rd and 11th terms of this AP is the same as the 3rd, 2nd and 1st term of a geometric series. Find the first term of the geometric series. I have constructed 4 equations from this a_p = a_q r^2 a_p+2d...
  10. E

    Mental Arithmetic: Solve 314*159 & Discover Speciality

    (a) Calculate this in your head: 314*159 (b) What's so special about these digits? I would like to see how people solve this in different ways.
  11. J

    Clock/modular arithmetic anyone?

    anyone familiar with this, along with some RSA and calculating large powers with modular arithmetic (im lost at the name of it currently). i have attached the test that I took last week ... he allows us to take home the exact same test home, and do it again, and he combines the grades ...
  12. G

    Why Does Integer Arithmetic in Haskell Seem Inconsistent?

    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...
  13. M

    Day of the Week Puzzle: Solving with Modular (Clock) Arithmetic

    I have this question and you need to use Modular (Clock) Arithmetic to solve it. If there is any work I need to know that. If you don't know the answer, is there anyway you can just tell me the process of how to do it? Thank you very, very much! Here is the problem: What day of the week...
  14. D

    Modulo arithmetic (?) question

    Find all integers n>1 such that n is a power of 3, and n-1 is five times a power of 2. Can anyone give me a push in the right direction?
  15. N

    Arithmetic Sequence Series Problem

    Hi. Please explain to me how to do these three problems: 1. The terms x+3, 3x-1, and 7x-2 are consecutive terms in an arithmetic sequence. Find x. 2. The sum of the first twenty-eight terms of an arithmetic series if the sum of the first twelve terms is -72 and the sum of the first...
  16. R

    Can someone explain the reverse sum in arithmetic series?

    Please can someone help me with arithmetic series. I don't understand why you reverse the sum when summing 1 to 100. also I don't understand the formula given : sn = n/2 ( 2a+(n-1)d ) thanks Roger
  17. N

    Arithmetic progression(alternate method)

    in an arithmetic sequence there is an even number of term's the sum of terms in the odd places is 440 and the sum of terms in the even places is 520, the last term is bigger than the first term by 156 find how many term's the arithmetic sequence has. This was from a previous post, but i...
  18. A

    An arithmetic progression problem

    in an arithmetic sequence there is an even number of term's the sum of terms in the odd places is 440 and the sum of terms in the even places is 520, the last term is bigger than the first term by 156 find how many term's the arithmetic sequence has.
  19. K

    Is (2n-1)! Always a Square Modulo 2n+1?

    Show that (2n-1)! is always a square modulo 2n+1. :cry:
  20. M

    Geometric Sequence; Arithmetic Sequence w/o 2,3,7

    Problem 8. Find x & y if the sequence 2y, 2xy, 2, xy/2,...is geometric. Problem 9. Find an arithmeitc sequence none of whose terms are divisible by 2, 3, or 7. Prtoblem 10. Consider two arithmetic sequences: A:3, 14, 25.. B: 2, 9 , 16, ... Write the first five...
  21. K

    Modular Arithmetic, and systematic approach.

    Hi, Can somebody drill me on the "congruences and modular arithmetic"? I know it is a big topic, but I think I am missing "something" in my knowledge... These things seem very unusual to me, and makes no sense sometimes. Find smallest integer n, where: 3^n \equiv 1 (mod 7) Is there a...
  22. E

    Understanding x=pmodn: An Integer Modular Arithmetic Primer

    What does x=pmodn mean where x,p,are integers and n is a natural number?
  23. C

    How do I solve problems with decimals using 2's complement arithmetic?

    How do you do this problem? Sum of +17.5 (Base 10) and -43.25 (Base 10) using 2's complement arithmetic. Difference of +17.5 (Base 10) and -43.25 (Base 10) using 2's complement arithmetic. The binary representations must have 12 digits. How the heck do I solve a problem with decimals like...
  24. D

    What is the fifth term in this arithmetic sequence?

    The first four terms in an arithmetic sequence are x+y, x-y, xy, x/y, in that order. What is the fifth term? Can anyone show me how to do it? O btw, the fifth term is a number, is not a variable Thx
  25. A

    How to Calculate the Mass of a Calcium Atom in Kilograms?

    ok, I'm trying to get the mass of a calcium atom in kilograms...formula for converting atoms to grams is(1.00amu=1.66x10^-24g)Calcium is 40.1amu Ok, here is the setup with it.. 40.1amu/1 x 1.66x10^-24g/1.00amu x 1kg/1,000g= ... So how am i suposed to get the answer? Could someone please put...
  26. W

    Question in Discrete Math: Modular Arithmetic

    Hello, I am currently taking a course which has exercises/questions whose solutions are based on discrete mathematics. For anyone interested, the link to the course is: http://www.math.uAlberta.ca/~tlewis/222_03f/222_03f.html We are encouraged to discuss these problems with others...
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