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

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136 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 ...
3
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1answer
166 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
106 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. ...
0
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1answer
197 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 ...
0
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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
3
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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 ...
1
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1answer
56 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 ...
1
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1answer
81 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 ...
2
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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 ...
3
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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 ...
3
votes
4answers
280 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
462 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 ...
2
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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
186 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 ...
25
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2answers
864 views

How to define addition through multiplication?

One might define multiplication $\bullet$ on $\mathbb Z$ as follows: $\bullet: \mathbb Z\times \mathbb N\ni (a,b) \mapsto a+\cdots+a\in \mathbb Z$ where we add $b$ times. But suppose we are in a ...
0
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1answer
74 views

Matrix vector addition

Given A a 3x3 matrix and B a 3x1 matrix (or column vector), I am asked to calculate A + B. Both are initially filled with one's. To my knowledge the two matrices would have to be of the same n×m ...
10
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3answers
855 views

What's the difference between $3^{3^{3^3}}$ and $27^{27}\;$?

Why does $\;\large3^{3^{3^3}}\;$ evaluate to a larger number than $\;\large 27^{27}$?
2
votes
1answer
88 views

Cubes, squares and minimal sums

I have trouble solving the following task: i need to find positive integers a and b such that 1) $a \neq b$ 2) $ \exists c \in \mathbb{N} : ~ a^2 + b^2 = c^3$ 3) $\exists d \in \mathbb{N}: ~ a^3 + ...
2
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1answer
73 views

Maximal sum of positive numbers

I'll be grateful for any help with the foollowing question. I think the solution must be easy enough but i haven't figured it out yet. Let a and b be positive integers such that 1) $\exists c \in ...
1
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1answer
362 views

Sum of the first k binomial coefficients for fixed n

I am reading Remarks on a Ramsey theory for trees by Janos Pach, Jozsef Solymosi and Gabor Tardos. Let $k, d, n \geq 2$ be integers. Somethig interesting happens when $$2^{n/k} > \sum_{i=0}^{d-1} ...
4
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2answers
139 views

$5 \frac {3}{*} \times 3 \frac {*}{2}=19$?

One of my friends gave me this apparently easy-looking problem which I do not know how to crack. The problem is to find the values of "*" where $$5 \frac {3}{*} \times 3 \frac {*}{2}=19\text{ ?}$$ ...
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5answers
6k views

Finding a number given its remainder when divided by other numbers

I have this GRE question that I'd like to know how to solve. I want to solve it in as simple a way as possible, since it is GRE material. In particular, I don't want to use "congruences" or modulo ...
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2answers
37 views

Working out the interval in which the algae becomes extinct (how to get the interval)

I have a birth rate that is $$b(p) = \frac{p^2}{p^2 + 3}$$ and a death rate that is $$d(p) = \frac{p}{4}.$$ I therefore have a reproduction rate as $r = b - d$. In order for my algae to become ...
0
votes
2answers
115 views

What two kind of decimals you times together to make 1?

Are there any decimals that times to make 1? I know that 0.25 x 4 = 1 but it's a decimal and a number. I need two decimals. Any ideas? I'm not an expert btw so... thanks
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3answers
67 views

Solving the algebraic equation

I am trying to solve this: $$x-40={-400\over x}$$ The answer must be $x=20$ Please give step by step explanation.
3
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2answers
199 views

Why $x^{(1/2)2} \neq x^{2(1/2)} $?

I know, probably is a newb. question, but i can't get this $x^{(1/2)2} \neq x^{2(1/2)} $ $ x\in\mathbb R^+$. I know $x^{(1/2)2}=(\pm \sqrt{x})^2=+x $ and $x^{2(1/2)}=\pm x $ because ...
2
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1answer
619 views

Complex division: polar form vs complex conjugate

The original problem In an electricity course which I volunteered to help with, the students solve circuits using phasors. Using phasors requires a good knowledge of complex numbers arithmetics, ...
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2answers
841 views

Chopping arithmetic on terms such as $\pi^2$, $\pi^3$ or $e^3$

I have a problem where I have to use 3-digit chopping with numbers such as $\pi^2$, $\pi^3$, $e^3$, etc. If I wanted to 3-digit chop $\pi^2$, do I square the true value of $\pi$ and then chop, or do ...
1
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1answer
733 views

Reverse mod operation getting bounded number

Is it possible to get the reverse of the mod operation if I just want the first possible number? I mean, if I can bound the initial number. For example: I want to do $(x+y) \pmod {10} = z$ ($x$ ...
0
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1answer
53 views

Addition and multiplication of two numbers.

At this point I have to find out the maximum number of digits I can get when I multiply 2 numbers with m and n digits. I am not ...
3
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4answers
134 views

Is there a term for $x^{1/4}$

The square root of $n$ is $n^{1/2}$ The cube root of $n$ is $n^{1/3}$ Is there a term for $n^{1/4}$ Or would you just say 4th root or something? Update: I'm asking if there's a term for this ...
0
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1answer
173 views

Are there statements in set theory about arithmetic beyond the reach of the analytical hierarchy?

Even if the answer were negative for arithmetics(I have no idea), in the more general case: Can any mathematical statement be expressed as a $\Delta_m^n$ (with n, m belongs to N) statement in a chosen ...
18
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1answer
533 views

Are the real numbers ever needed to prove a property of the natural numbers?

Suppose no one had invented/discovered the real numbers yet (so e.g., no calculus), would this constrain the possible theorems or knowledge we could have about the natural numbers?
3
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2answers
36 views

Does this equality hold?

Is the following proposition true for real numbers? $$\frac{\sqrt{2|x|-x^2}-0}{x}=\begin{cases}\sqrt{\frac{2}{x}-1}&,\;\;\;x>0\\{}\\\sqrt{-\frac{2}{x}-1}&,\;\;\;x<0\end{cases}$$ I ...
0
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2answers
112 views

Aproximate calculation in decimals

I am trying to refresh on precision of calculations. If we have the decimal fractions: $.234673$, $.322135$, $.114342$, $.563217$ each known to be correct to six figures why are each of the decimals ...
1
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1answer
187 views

Iteration of the function $d(n)=a-n$

I start by defining the function $f$ $$f(0)=0,~~~~~f(n+1)=d(f(n))=a-f(n)$$ So: $$f(n)=d^{\circ n}(0)$$ $f(1)=a-0=a$ $f(2)=a-(a-0)=0$ $f(3)=a-(a-(a-0))=a$ How can I find the solution of $f(x), ...
13
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3answers
373 views

Is there an numeric arithmetic with a single operator?

I remember reading a while back about arithmetics with only a single operator that did all the work of the familiar $+ - \times /$ operators. If there is such a thing, could someone point me to it? ...
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6answers
451 views

What is the difference between $0$ and $-0$?

Why is there a $0$ and a $-0$? I thought zero meant nothing, so how can we have negative nothing?
2
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3answers
2k views

Is there a number which is a perfect square, cube, fourth power and so on?

as the title asks, is there an integer which is a perfect square, cube, fourth power, fifth power, etc until, well, it's a tenth power per say? Are there integers that are squares, cubes, and so on ...
2
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4answers
391 views

Numbers ending with 0 [duplicate]

$2n$ ends with $0$ if $n$ ends with $0$. So how can we know if 2n ended with 0 in the first place?
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2answers
58 views

How to distribute points to players based on their effort?

Assume that a HOME team and an AWAY team play each other in a game. The HOME team defeats the AWAY team, so the HOME team gains 30 points and the AWAY team loses 30 points. Each team has two players. ...
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3answers
69 views

sum of consecutive arithmetic progressions

I was facing the following problem: if $a, b, c$ are natural numbers in order and in a arithmetic progression with R=2, and $a^2 + b^2 - c^2$ = 0, what is $a+b+c$?
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1answer
95 views

An identity involving the powers of a nilpotent element in a unital commutative ring

Suppose $R$ is a commutative unital ring with identity $1$ such that the equation $nx = 1$ has a unique solution for each integer $n \ge 1$, and let $\xi$ be a nilpotent element of $R$ with nilpotency ...
2
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3answers
174 views

551 used items, it takes 6 used to create one new… how many new items can you make?

I had this question recently in an online exam that really confused me (it's not hard). A business decided to recycle all their old paper cups and produce new ones from the recycled cardboard. For ...
12
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4answers
383 views

$ \sqrt{2-\sqrt{2}} $ simplified

So I have a (nested?) square root $ \sqrt{2-\sqrt{2}} $. I know that $ \sqrt{2-\sqrt{3}} = \frac{\sqrt{6}-\sqrt{2}}{2} $. I know how to turn the simplified version into the complex one, but not vice ...
0
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1answer
104 views

Can the arithmetical hierarchy (AH) be defined in weaker (than PA) systems of arithmetic?

such as Q, PRA, EFA, Presburger, or any others out there. I am a little confused here. They are all systems described in the language of first-order logic. The only differences among them are in the ...
2
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1answer
516 views

Notation for multiple of a number?

I've have a question about the notation for a multiple of a number, I know you can write it several ways: $2|4, 4 = 2n $ where $n$ is an integer, etc, but what about this one $$4 = \dot 2$$ I've ...