Questions tagged [arithmetic]
Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag. Questions about number theory (sometimes called "arithmetic") should not use this tag and should instead use (number-theory) or (elementary-number-theory).
6,177
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Arithmetic progression, find $a_1$, $d$ and $n$. [closed]
$$\begin{cases}
a_1+a_2+a_3 = 24 \\
a_2^2 - a_1 \times a_4 = 10 \\
S_n - S_4 = 23
\end{cases}$$
Searching for $a_1$, $d$, and $n$.
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How to prove that this two fractions are not equivalent (equal)?
We have the fractions $\frac{n+3}{n-2}$ and $\frac{2n-3}{2n-8}$. Prove that these fractions are not equivalent (equal with each other)
My ideas and what I tried:
I tried to multiply the terms $(n+3) \...
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1
answer
43
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Determine x,y if they are integers number [closed]
Determine x,y who belongs to Z(integers number) if xy+x+y=3 and (x+1)(y+1)=4
I tried to make an equation system ,to equalise them , but I couldn't bring them to a ' easier form".
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0
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37
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Confusing with basic arithmetics, BODMAS
What is the result of $6\div 2(1+2)$?
I simplified the bracket with the $2$ outside first and my final answer was $1$.
But I'm kind of getting confused because alpha mathematica evaluates this same ...
4
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1
answer
46
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Does $\omega$-consistency depend on the encoding?
A given theory $T$ can interpret the language of arithmetic in different ways, and therefore it seems to me like it is possible that in one of these ways $T$ would be $\omega$-consistent but not in ...
- 502
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2
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87
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Why doesn't $x^0$ equal the same thing as $x\cdot0$?
If $x\cdot0$ means adding zero $x$s together and $x^0$ means multiplying zero $x$s together then conceptually why aren't they both equal to the same thing?
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65
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How Do I strengthen my Math basics? [closed]
I am 28 year old adult. I was good at Math when I was in school in my 6th Grade. I had a bad relationship with my Math staff, since then I hated math. And as an outcome, I started struggling with even ...
- 21
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1
answer
62
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Modulus with negative number
Modular arithmetic with positive Integer can be describe with clock system where we usually wrap an number with an number like 13 that warp the number of 1. But how if in modular arithmetic use an ...
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0
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46
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How does two negatives equal a positive without distributing? [closed]
Basically I was asked how two negatives equals a positive when looking at the most basic way of multiplying (doing manual addition). The example given was $2\times 2$ is the same as $2+2$ but $(-2)\...
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2
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2
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How would you go about finding the exponent for any given x that most closely matches or surpasses factorial growth?
While analyzing the factorial function and comparing it to basic exponentiation, I couldn't help but notice the obvious fact that exponentiation can eventually overtake factorialization if the ...
1
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2
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89
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Double summation manipulation
How to prove the equivalence between these two double sums? Probably it is a stupid task, but I cannot solve it.
Let $k\in\mathbb{N}$, prove that for every $\alpha,\beta,s_i\in\mathbb{R}$ it holds
$$
\...
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56
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Primes in Quadratic Extensions $K$ of the Ring $\mathbb{Z}$ [duplicate]
While studying Arithmetics, I came across an interesting theorem on the properties of primes in a quadratic extension $K$ of the ring $\mathbb{Z}$.
The theorem writes as follows:
Let $x\in K$. If $N(...
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35
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If there are 29 vehicles per one square kilometers, how many square kilometers per 100 vehicles are there?
29 vehicles/$km^2$ means (1/29) $km^2$/(1 vehicle)
Per 100 vehicles there are 1/2900 $km^2$.
Whatever you sq kilometers are you have to divide by 100 moto vehicles
100/29 $km^2$/100 vehicles
(100/29)/...
user1218223
1
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1
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135
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Complex numbers and congruence, article by G.B. Mathews
I am reading "Notes in connexion with Fermat's last theorem", by G. B. Mathews. (accessible per example on Google books)
For some integer $k$, he defines $r = e^{\frac{2 \pi i}{k}}$ and: $$ ...
- 176
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0
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15
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On Elkik's Theorem of Henselian pair.
As far as I know, the celebrated Elkik's result often quoted boil down as follows$\colon$ Let $A$ be a heneselian local ring with its maximal ideal ${\frak m}$ and choose an arbitrary ideal $I \subset ...
- 853
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1
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55
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Do Idoneal numbers give infinitely many primes?
Euler famously showed that there are at least 65 idoneal (convenient) numbers. This was Euler's definition of idoneal number:
The number $n$ is idoneal if the following holds: Let $m>1$ be an odd ...
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1
answer
78
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Is the fractional part of a real number has to be greater than or equal to 0 but less than 1?
https://en.wikipedia.org/wiki/Fractional_part
I was reading the definition of fractional part, but I have not understood something and I want to make sure.
Is the fractional part of a real number has ...
- 65
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0
answers
48
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Binary operation vs binary operator in basic arithmetic
Talking about the 4 basic operations (addition, subtraction, multiplication and division), what is the difference between a binary operator and a binary operation?
https://en.wikipedia.org/wiki/...
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2
answers
84
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Are the operators of the four basic operations of arithmetic binary operators? [closed]
Supposing I have a subtraction (multiplication and division) of 3 or more numbers, e.g., 20 - 3 - 2 - 3 - 1, will the subtraction end up being done in pairs, i.e., the - operator is ...
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1
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44
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Binary operators - Add More Than 2 Numbers
If I have the sum of 3 or more numbers, e.g., 1 + 2 + 3 + 50, will the sum end up being done in pairs, i.e., the + operator is binary and thus only supports 2 operands at a time?
I am new to algebra, ...
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1
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Associative property of addition - Binary operators
The associative property of addition says that it does not matter how we group the addends when we add 3 or more numbers. My question is, does addition only operate ...
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1
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90
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Defective clock questions - Watch gaining 3 minutes every hour
An analog watch gains 3 minutes every hour. If it is set right at 11 a.m. on February 21st, 2012 when will the hour hand of this defective watch and a correct watch be at the same position ?
My ...
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1
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27
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Fractions and linearity
Imagine that the price of a good is given as $5$/unit. Mathematically,
if we are to compute how much we can buy with 1\$, this would just
be 1\$/5\$ per unit=0.2 units. However, this computation ...
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1
answer
23
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Schedule recurrent tasks to match a desired frequency?
I'm trying to write a small task scheduling function that takes a list of tasks, each with an assigned priority. These tasks are meant to update some values in a database, and some need to run more ...
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2
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124
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What does $(4 \mod 100) \equiv (5 \mod 99)$ mean?
I came across the following example on page 9 of Introduction to Arithmetic for Digital Systems by Waser and Flynn:
Example 1.5
Suppose we have two $\mod 99$ $A'$ and $B'$, having the following ...
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1
answer
53
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Difficulty in solving the most famous online ( 8÷2(2+2) question with 2 different approaches [duplicate]
For the problem 8÷2(2+2)
I have found two approaches to solve the problem.
1st one is:
$\frac{8}{2(2+2)}$
This looks like a direct approach ad we got 1 as answer.
2nd one is using BODMAS:
8/2(2+2)
8/2(...
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0
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31
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Using modular arithmetic to explain end around carry
I understand that end-around carry occurs because the diminished-radix complement coding has two representations of zero, but I'm having trouble understanding how it follows from the rules of modular ...
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1
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51
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Natural numbers ($2\leq n$) divided into two sets. I'm trying to find characterization of these sets.
Here is tiny program that finds biggest prime divisor of a number (function find), written in pseudocode (Project Euler 3rd exercise, original source in C language ...
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1
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68
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If you need 3:2:1 ratio of X,Y,Z to make a something, doesn't that mean you need 6 units:4 units:2 units to make two units of that thing?
Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing.
If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of ...
user1208473
0
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0
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110
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Question on a finite sum
I have a simple question regarding a particular form of a sum and I was hoping someone could provide some insights or guidance.
if $n\:=\:\sum _{k=1}^n\frac{g\left(n,k\right)}{f\left(g\left(n,k\right)\...
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1
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39
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Evaluate the definite integral of a piecewise function over two intervals.
NOTE: I need help in solving this integral. I am new to calculus and this expression looks to complicated and I am unable to simplify it.
Solve: $$\int\limits_{x=0}^{ \sqrt[4]{\frac12}} \left( \sqrt[4]...
2
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4
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Is $\sqrt 3 + \sqrt 2$ a surd?
Is $\sqrt 3 + \sqrt 2$ a surd?
By definition an irrational root of a rational is called a surd.
Easy to observe that $\sqrt 3 + \sqrt 2$ is irrational. If not, $\sqrt 3 - \sqrt 2$ being the reciprocal ...
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3
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Does the limit of these sums converge/diverge?
I am looking at these two sums:
$$s_N=\sum_{n=0}^N\frac{\sin n}{n!}x^n, \qquad \text{and} \qquad c_N=\sum_{n=0}^N\frac{\cos n}{n!}x^n, \quad \text{for} \quad x\in \mathbb{R}. $$
I am interested in the ...
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How Do You Practically Calculate Common Percentages?
I was wondering if there is any quick way of calculating some common percentages such as $15\%$, $25\%$, $50\%$, $75\%$, $90\%$ etc.
The best think I could come up with is just simplifying the ...
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1
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Help understanding how to Evaluate divisions [closed]
Morning to everyone,
I am trying to understand a problem I came across, which I can solve but I still do not understand the logic behind it.
The problem is as follow
Input: equations = [["a"...
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1
answer
139
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On the Axiomatic Foundation of Elementary Number Theory
I am under the impression that there is a set of axioms on which elementary number theory unfolds. If this is true, what are the axioms? Are they the five Peano axioms (at least, thought there were ...
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2
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What is a combination of the numbers 1, 2, 3, 4, and 5 that yield 170, using only basic operations (+, -, *, /, ^) and the factorial (!)?
Rules:
Only basic operations (+, -, *, /, ^) and the factorial (!) are allowed.
No concatenation (i.e. 34, 12, 125, etc).
Parentheses are allowed.
All numbers must be used (omitting numbers is not ...
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1
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83
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How is the arithmetic multiplication related to tensor products?
Mathematical objects are supposed to "model things", sometimes, more mathematics. In this sense, i think is "natural" to assume that tensors, being such universal objects as they ...
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1
answer
87
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How PEMDAS,BODMAS are true in this case [closed]
If we look at this expression
$\frac{A}{B + C}$
It looks like it is simply
$A ÷ B + C$
But the calculator does it as
$A ÷ ( B + C )$
Why does the calculator do it like this as in the first place there ...
0
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0
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Fixed part of the induced representation. ntation.
Suppose the topological groups $h, G$ satisfy that $H < G$ and that $[G \colon H] < \infty$. Let $V$ be a $K$-vector space on which $H$ acts continuously. Then we consider the induced $G$-...
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Is it possible for integer division in C++ to express a compact mathematical condition, as for Euclidean division?
I am studying integer division in C++. At the same time, I read the wikipedia article 'Euclidean division'. In this article there is such a lemma:
...
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1
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65
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What is the fastest way to perform mental division? [closed]
I am looking for a way to divide relatively small numbers with high accuracy, though I can't seem to find a way around long division. For instance, say we are trying to convert $7/11$ or $23/17$ to a ...
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2
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Sum of the digits of $2001^{10}$
I saw this question in internet and I could not solve it.
I saw that many people are trying to solve these kind of questions by Python. Then I decided that this question is a computer-science kind of ...
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1
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If $ABCDE\times4 = EDCBA$ where $A, B, C, D, E$ are all distinct. Why can't $E$ be $3$? [closed]
If $ABCDE\times4 = EDCBA$. Here $A, B, C, D, E$ represent distinct nonzero digits and $ABCDE$ and $EDCBA$ are five digit numbers. Why can't E be three?
user1202451
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Specialized algorithms for edge cases of binary arithmetic
I have several mathematical operations on binary numbers that are special cases of more general arithmetic operations. I am wondering whether there exist more specialized algorithms purpose-made for ...
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0
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77
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Can you beat every Tax Collector game?
There's a one-player math game called Tax Collector, and recently I was intrigued by it. Let me explain the game, and then I'll ask my question.
To start, choose a number to be your ceiling - the ...
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16
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Did I do this estimation correctly?
I was looking online for cars with APR rates just to see if I can find the monthly and yearly interest. Just to practice what I know, and I want to see if I did this correctly.
2023 Chevrolet Camaro ...
3
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0
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64
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Is there a transfinite version of Post's Theorem?
Let $\emptyset^{(n)}$ denote the $n$th Turing jump of the empty set. Post's theorem states:
A set $B$ is $\Sigma^0_{n+1}$ if and only if $B$ is recursively enumerable by an oracle Turing machine with ...
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3
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118
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Failure of AM, GM inequality while trying find the minimum value of a function.
The expression whose minimum value I'm trying to find is:
$$\displaystyle\frac{{ \sec{⁴}\alpha}}{{ \tan{²}\beta}}+\frac{{ \sec{⁴}\beta}}{{ \tan{²}\alpha}}$$
I know there are many more methods to find ...
0
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1
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42
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If $-2\le x \le 1$ and $-3.4\le x-y \le 3.4$ and $a\le y \le b$ find $a$ and $b$
I have a question, if $-2\le x \le 1$ and $-3.4\le x-y \le 3.4$ and $a\le y \le b$ find $a$ and $b$.
that's how I did it:
if $-2\le x \le 1$ then $-1\le -x \le 2$
$$-3.4-1\le x-y+(-x) \le 3.4+2$$
$$-...
