Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, radicals, etc.

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Smallest Mersenne prime with 100 million digits?

As some of you are probably aware, the Great Internet Mersenne Prime Search (GIMPS) is managing the search for the largest Mersenne primes of the form $M_p=2^p-1$, where $p$ is itself prime (GIMPS ...
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4answers
1k views

Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$

I am stuck on this homework problem! Prove that if $x$ and $y$ are real numbers such that $0<x<y$ , then $\sqrt{x}<\sqrt{y}$. This is in a chapter involving the least upper bound axiom and ...
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2answers
474 views

Floor function inequality of multiplication

In a final step of a homework, I want to deduce that $$n\lfloor(n-1)!e\rfloor+2\le \lfloor n!e\rfloor+1$$ I'm unable to see whether this is true in general that $$n\lfloor a\rfloor+1\le \lfloor ...
2
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1answer
38 views

Proportionality In two Values Equal to $0$

If two values $m$ and $n$ are in direct variation, then $m \propto n$ If the constant of proportionality is $q$ between them, then $m = qn$ If $m$ and $n$ both are equal to zero or $m = ...
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3answers
664 views

How to manually calculate Roots

I have always used a calculator for determining roots But I think it would be useful to know how to do this on paper. Are there different procedures for calculating square roots then cubic roots or ...
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1answer
67 views

Arithmetic and geometry [closed]

While $3^2 + 2^1 = 11$ arithmetically, geometrically aren't you adding a line of length $2$ to a square of area $9$, so wouldn't the geometrical answer be $9$, because adding a line to a square would ...
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2answers
100 views

Absolute Value of $|-3 -2|$

$|-3 -2|$ is the distance between the points $-3$ and $-2$. If we solve it further then, in one way I get $|-5| = 5$. But $5$ is the distance between $0$ and $-5$ in this case. In other way, $2 ...
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2answers
84 views

Absolute Value Problem, Solution and Method

Please check my method and also if I have solved the following problem correctly: Problem: $f(x) = |x - \frac12| + |x + \frac12|$ If $x = -1$, then: $f(-1) = |-1 - \frac12| + |-1 + \frac12|$ From ...
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2answers
88 views

How is the following arithmetic sequence solved?

Apologies to bother you with this, but how is the following arithmetic sequence solved? $$\dfrac1n \left(\sum_{k=1}^{n-1}\dfrac{n-k+1}2\right)$$
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3answers
1k views

Positive and negative square roots

If the number $13$ is squared it gives $169$. Then if we take the square root of $169$; $\sqrt{169}$ it gives $13$ and $-13$. Why is this so if we know that $13$ was positive and it was multiplied by ...
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3answers
5k views

How can I use prime factorization to find a cube root?

This is based on a lesson at Khan Academy that I didn't understand. In the lesson, the instructor uses the number 512 as an example and the entire prime factorization consists of three groups of ...
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1answer
54 views

Need help to create formula/equation

I am looking to try create a formula/equation(I am a novice). I'll use a fictitious example that has to do with basketball. Assume there are 5 players that score in each game for each team. Team A: ...
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2answers
120 views

When is a fraction simplified?

When is a fraction simplified? "A fraction is simplified if the numerator and denominator do not have any common factors other than 1." This is what I read on this website: ...
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2answers
131 views

Repeating Square Root Closed Form [duplicate]

I've been thinking about repeating square roots: $\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}$. I wrote a program on my calculator to do it $n$ times and I found that, if $x = y^2 - y$ then ...
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6answers
327 views

Solve the equation $x-7=28$ [closed]

The question is $x-7=28$ But I'm not sure if when I subtract do I have to change the signs to negative?
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2answers
109 views

how to show that a function$f$ is contained in all natural numbers?

Let $f:\mathbb{N}\times\mathbb{N}\rightarrow \mathbb{R}$ be defined by $f(a, b) = \frac{(a+1)(a+2b)}{2}$. Carefully show that the image of $f$ is contained in $\mathbb{N}$.
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1answer
267 views

Converting solution of linear equations to slope intercept form

I will use a very simple linear equation to make my point: $$3x = 2$$ $x$ will always be equal to $2/3$. This equation in itself has no use in graphing. So if we want to be able to apply that ...
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1answer
72 views

Addition with sets and integers

I've been looking all over the internet for an answer to this question, but it usually just brings up Python related subjects and not anything remotely close to my question. I basically want to know ...
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1answer
48 views

Obtaining the total from a percentage

$x$ is $20$ percent of $t$. t=?; //to compute x=198; Example compressed = 64; uncompressed = (100 / 20) * 64; //is it ...
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4answers
257 views

Is the following statement true? Why?

$\frac{a}{b}\neq0 \Rightarrow (a\neq0\land b \neq0)$ At first sight that seems quite obviously true, however, wouldn't $b = 0$ also fit the condition? $\frac{a}{0}\neq0$
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2answers
190 views

Dividing a number by zero [duplicate]

Why can't you divide a number by zero? It is possible to say $\sqrt{-1}$ is an imaginary number $i$, but why can't you say $\frac{1}{0}$ is also an imaginary number $z$ (for example)?
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52 views

find the number b where a = b + 19% of b

Find which number plus its 19% gives for example 200, 233 .. Story short: for example I have the number 0.30 now I need to know with formula how can I get which ...
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1answer
36 views

Calculate total number of matrices of all orders which contain $2013$ elements

Calculate total number of matrices of all orders which contain $2013$ elements My Try:: By Simple Guessing wecan say that there are two matrices of order $(1\times 2013)$ and $(2013 \times 1)$ ...
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2answers
65 views

How do I append an integer to the left of another integer?

For example: . is my append operator f(x,y) = |x| . |y| f(1,45) = 145 f(233,10) = 23310 f(8,2) = 82 f(0,1) = 1 This is a trivially easy problem to ...
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1answer
71 views

Problem about a simple division

My little sister wants me to divide $135628$ by $339$. I can not make her understand that quotient is $400$ and remainder is $28$. She does not understand how one last $0$ comes after $40$. She knows ...
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111 views

Can all programs reducible to ones with only arithmetic operations on inputs be simulated with polynomial overhead by arithmetic machine?

In Can all programs be modeled as operations of elementary arithmetic operations on inputs? and computabiltiy theory, I asked: we treat all inputs and intermediate results and final outputs as ...
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94 views

Can all programs be modeled as operations of elementary arithmetic operations on inputs?

In mathematics and computabiltiy theory, we treat all inputs and intermediate results and final outputs as natural number. While algorithms/programs themselves are considered natural numbers, here we ...
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3answers
110 views

Repeated nested roots

Quite some years ago, I remember being asked the following question: Suppose $\alpha = \sqrt{2+\sqrt{2+\sqrt{2+\ldots}}}$, what is $\alpha$. The solution was given by squaring $\alpha$ and solving ...
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1answer
59 views

Get back the original value of width and height from rounded values

I have this calculation for resizing an image in my site. Here is the sample code: ...
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2answers
130 views

Division with negative exponents

I have a problem that looks like this: $$\frac{20x^5y^3}{5x^2y^{-4}}$$ Now they said that the "rule" is that when dividing exponents, you bring them on top as a negative like this: ...
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4answers
680 views

Problem related to a clock

I faced the following problem: At what time after 4 o'clock, the hour and the minute hand will lie opposite to each other? $\quad$ 4-50'-31" $\quad$ 4-52'-51" $\quad$ 4-53'-23" ...
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215 views

What is the square root of $i^4$?

What is the $\sqrt{i^4}$? $i^4$ = $(i^2)^2$ So is $\sqrt{i^4}$ = $\sqrt{(i^2)^2}$ = $i^2$ = $-1$? Or is $\sqrt{i^4}$ = $\sqrt{1}$ = $1$? When I plug it into my TI-89 Titanium, I get $1$. Edit: I ...
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4answers
5k views

Why can't you add terms with different exponents?

When evaluating algebraic expressions, 1) you can add together like terms. $3x^5 + 6x^5 = 9x^5$, but you cannot add together different terms: $2x^4 + 3x^5$, because these have different exponents. ...
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1answer
137 views

What is the minimum number of blocks to build this?

A rectangular solid is built using $N$ cubes of a side length of 1cm. When viewed from such an angle such that only 3 of the sides of the rectangular solid are visible, there are 231 $cm^2$ of area ...
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1answer
170 views

Efficiency in factoring lists of consecutive numbers

Suppose I'm looking at prime factorizations of numbers in the vicinity of this one: $$ 1354 = 2 \times 677 $$ The smallest prime appears here, and the next prime after that does not. Going one step ...
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2answers
2k views

How to find multiples of numbers under a certain range

I recently found a 'question' that requires me to find the sum of all multiples of 3 and 5 under 1000, I sadly cheated and found some code online to help build a code in python: ...
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1answer
107 views

A Cryptarithm Problem from Gelfand's “Algebra”

The following problem is from the very beginning of the book and it even has a solution with explanation. However, I keep banging my head against the wall unable to understand the reasoning behind it. ...
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1answer
206 views

How to solve a cryptarithm with multiple conditions

I'm trying to solve a cryptarithm that must meet all of the following conditions: one + one = two seven is prime nine is a perfect square More specifically, i'm trying to find the ...
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1answer
64 views

why imaginary numbers have a a different meaning than $R^2$ if they are semantically equivalent?

why imaginary numbers have a a different meaning than $R^2$ if they are semantically equivalent? regardless of the historical perspective, we know that ther is no semantic difference between them
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3answers
57 views

Mod question: $2^{-1} \bmod 5 = 3$

According to Wolfie: $2^{-1} \bmod 5 = 3$ http://www.wolframalpha.com/input/?i=2%5E-1+mod+5 Why is that?
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2answers
73 views

Basic calculation with root roots and power

Sorry for the boring question but I just need someone to remind me the way to calculate this: $\displaystyle \left(\frac{a}{2}\right)^2 + x^2 = a^2$ (i used carrot sign cause i dont know how to do ...
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1answer
59 views

Ratios without algebra? Surely not trial and error?

A 10 year old wants to learn about proportions but has no algebra background: Their questions is: 30 Kids go on a school trip Cost of the trip (t) + a lunch (l) =5pounds Kids who go ...
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1answer
88 views

I have a number and the percentage this number represents - how do I calculate what the full value is?

I have two known values : A sum and a percentage. I know that the sum is $16 000$, and this is $28\%$ of unknown value. How do I calculate what this value is? Like; $16000$ is $28\%$ of $x$? Doing ...
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0answers
106 views

Clarification of variable values in Arithmetic Coding algorithm

I have been trying to follow this video to implement my own Arithmetic Coding algorithm in Java. I am having a bit of trouble figuring out what some of the variables in the video should be. For ...
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1answer
135 views

Static Arithmetic Encoding/Adaptive Arithmetic Encoding Algorithm

I'm trying to learn how to implement the Arithmetic Encoder algorithm for one of my classes. The thing is the notes we have explaining the actual algorithm are a bit on the confusing side. I have ...
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2answers
47 views

Are these expressions equal?

I'm reading a physics booklet on radioactivity and at one part during the calculations it says: $$A(0) = 6.0 \cdot 10^{23} \times \ln 2/(8 \times 24 \times 3600) = N(21) = 6.0 \cdot 10^{23} \cdot ...
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4answers
285 views

Prove that $2222^{5555}+5555^{2222}=3333^{5555}+4444^{2222} \pmod 7$

I am utterly new to modular arithmetic and I am having trouble with this proof. $$2222^{5555}+5555^{2222}=3333^{5555}+4444^{2222} \pmod 7$$ It's because $2+5=3+4=7$, but it's not so clear for me ...
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1answer
485 views

A simple dividation problem

I can solve the below question by putting the each possibility into the questions conditions but I want to find out the value without putting the possibility . The number m yields a remainder p when ...
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3answers
64 views

Constrictions on A.P with factorials.

There are five numbers $(a_1,a_2,a_3,a_4,a_5)$, such that they are in Arithmetic Progression. Given that $a_1$ and $a_2$ are factorials, is there a possibility that either $a_4$ OR $a_5$ is a ...
3
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3answers
189 views

Definition for multiplication [duplicate]

I am serious. What is the definition for multiplication ?. Every book and resources online(the one's I have seen) tells multiplication is repeated addition. But that's only some defintion that can ...