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.

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1answer
69 views

How to demonstrate that this may belong to integers

$\sqrt{(3x ^ 4-12x ^ 2)/16}$ How can I demonstrate that this can belong to integers? Can you show me? Please! (Without testing values)
1
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0answers
14 views

Growth rate in the “infinitely many” of a diophantine approximation problem

Let $\epsilon>0$ and $x_1,\ldots,x_n\in\mathbb R^n$ such that $x_1,\ldots,x_n$ are linearly independent over $\mathbb Q$. We know from the pigeonhole principle that there exists infinitely many $q=...
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votes
1answer
33 views

What is the amount if percentage is given? [on hold]

A 'laddoo' is made of $60\%$ flour, $20\%$ sugar and the rest is 'ghee'. What is the quantity of 'ghee' in $2$ kg 'laddoos'?
1
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0answers
20 views

Finding all Possible Dividends and Divisors for a Given Quotient [on hold]

I am attempting to find an algorithm or method that will allow me to find some/all of the possible pairs of dividends and divisors given only the quotient in the equation "dividend/divisor = ...
1
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2answers
28 views

Does significant figures make sense for percentages?

If I ask for a percentage with 2 significant figures, I mean something like $62\%$ or $77\%$, with no decimals. But what about percentages below 10? Do I have to write them like $5.6\%$ ajust because ...
1
vote
1answer
31 views

When given the difference between numbers, do we use the absolute value?

This question is more about wording than computation. The sum of the first number and the square of the second number is 18. The difference between the square of the second number and twice the ...
4
votes
1answer
94 views

Let $a,b\ge 0$ be integers such that $2^na+b$ is a perfect square $\forall n>0$

Let $a,b\ge 0$ be integers such that $2^na+b$ is a perfect square $\forall n>0$. Show that $a=0$. I have no idea how to start this problem since I don't see any arithmetic proprety that I can use ...
0
votes
1answer
40 views

How to calculate 'n' given basic operations like '(n + x) mod p = r' where 'x', 'p', and 'r' are known?

Is it possible to calculate n for a given x, p, r in different scenarios with basic operations such as ...
3
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2answers
142 views

Which one is bigger $100^{300}$ or $300!$?

How to find which one is bigger $100^{300}$ or $300!$ without using a calculator? I have tried it for whole 2 years but could not find it yet.
1
vote
2answers
69 views

The minimum timescales to reach a population of 1 Trillion people

First, consider that we exist in a Utopian society, no wars and no disease. A result of this Utopian society is that our technology has advanced considerably, improving healthcare and life expectancy ...
1
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2answers
33 views

pricing grid base calculation

I am useless at maths and have been trying to figure this out for ages. I am creating an website for a client which prices fabric based on square inch of material. Their supplier gave them the ...
0
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0answers
72 views

Brazilian Mathematical Olympiad (OBM) [closed]

In a slate are written the numbers $1,2,\ldots,10$. For any two numbers $a$ and $b$ on the blackboard we call $S(a,b)$ the sum of all numbers on the blackboard except for $a$ and $b$. One allowed ...
5
votes
3answers
249 views

Summing cube roots in fractions [closed]

I found this problem, and understand the solution, but do not understand why they made the first assumption. The problem: The first line of the solution says that: The cube root of $1$ plus the ...
2
votes
3answers
82 views

Distance between endpoints of parabola with length $80$

I've seen a question asked in an interview as following. How can be the distance indicated by question mark calculated? What are the ways?
2
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2answers
52 views

Finding the sum of the first 4 terms of a geometric sequence

The first 3 terms of a geometric sequence are, respectively, the 1st, 4th and 13th terms of an arithmetic sequence. Given that the first term of the geometric sequence is 3 and the common difference ...
1
vote
1answer
28 views

Clock problem (hands becoming coincident)?

If it’s 4 o clock now, how many minutes will pass before the minute and hour hand are in the exact same place? In the solution, they come up with the formula: x=20+5(x/60), where x is the number of ...
1
vote
1answer
20 views

How to work with jointly proportional variables?

Given that x is directly proportional to y and directly proportional to z and inversely proportional to w, if x=4 when (w,y,z)=(6,8,5), what is x when (w,y,z)=(4,10,9)? This was my working (sorry for ...
1
vote
6answers
59 views

What is the general formula for a sequence that is neither arithmetic nor geometric? [duplicate]

If a sequence is such that the next term is given by $a_n*a +b$, what is the general formula of the given sequence? e.g.: $-$ for $a=4,\;b=6$, the sequence is: $1,\quad1*4+6=10,\quad10*4+6=46,\...
1
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2answers
46 views

Arithmetic and Geometric sequences - Describe the following sequence

So I'm asked to determine the type of sequence below as well as state the $a$, $d$, and $r$ values. I know the answers to a, b, and c, but for the last one I'm confused as to what to categorize it ...
1
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0answers
18 views

Power residue when changing level

I am stuck with the following problem while reading a book: Assume $x$ is a $k$-th power modulo $p^a$ for a certain off prime $p$ and $a \geqslant 1$. Assume moreover that $p^{a-1} || k$. Is that ...
4
votes
2answers
110 views

How to round to algebraic integers in real quadratic integer domains

I feel like this question has been asked here before, but I'm not finding it. In an imaginary quadratic integer domain, it is very easy to round algebraic numbers to algebraic integers. For example, ...
2
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2answers
58 views

How is this read correctly (problem with brackets)? 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 }

How do you read this correctly, where are the brackets if you set them? 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 } Taken from: https://www.ietf.org/rfc/rfc3526.txt I have great problems ...
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0answers
28 views

Can this simplified arithmetical theory with a syntactically non reachable last natural be complete?

The following theory is coined in the language of arithmetic, however it differs in that the successor, addition and multiplication functions are not total functions. Also we add a new constant $L$ to ...
0
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2answers
52 views

what is (-1)^(2/3) [duplicate]

Google says that ${(-1)}^{2/3}$ is $-0.5+\frac{\sqrt{3}}{2}i$ but on socratic it says that it is 1. Which one is it?
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votes
2answers
31 views

How to show that sum of numbers is greater than zero given each number is positive [closed]

Let $a_1,a_2,...,a_n$ be the numbers each greater than zero, how could one proves that $$\sum_{k=1}^{n}a_k> 0$$ using an appropriate method of proof.
0
votes
2answers
37 views

Largest possible difference between two numbers

I came across this practise question for a government numeracy test: What is the largest possible difference between 10 & 20 to 2 decimal places? What is the answer? As far as I can tell, ...
1
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1answer
19 views

Attempting to reverse an additive function I've learned

EDIT 2: Used MathJax, now that I know it exists. So I discovered an easy way to add a succession of numbers together a while back, and I'm trying to reverse it for an RPG sheet in LibreOffice Calc. ...
1
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0answers
55 views

Is this theory of arithmetic with a last natural that is not reachable from below complete?

This theory is a theory of arithmetic having a last natural number that is not reachable from below by syntactical recursive iteration of the successor function. So it doesn't prove all rules of ...
3
votes
2answers
75 views

How to add negabinary numbers?

A negabinary is a number with a base as -2. I want to add two such numbers. I know how to convert them into the corresponding decimal numbers but wanted to add them ...
1
vote
4answers
89 views

Why is: $1+2+2^2+\cdots+2^{n-2} = 2^{n-1}-1$?

I know that this might be elementary, but I don't know how to prove this equality, some hint? I tried to extract the common two: $$ 1 + 2^1+2^2 + \cdots + 2^{n-2} = 1 + 2(1+2+\cdots+2^{n-3}) $$ But ...
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1answer
40 views

Exercise in floating point arithmetics. How large power can we get? [closed]

Say I have some polynomial $$P(x) = \sum_{k=0}^n c_kx^k$$ and double precision floating point numbers with mantissa part $53$ bits and exponent part $11$ bits. What is the largest magnitude of $x$ ...
1
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2answers
123 views

Elementary diophantine equations with unknown solutions [closed]

Solvability of a general diophantine equation has been proved undecidable. As a famous example of knowledge, we know that $x^n+y^n=z^n$ has no solutions (in $\mathbb{N}$) for $n>2$. As a famous ...
1
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1answer
25 views

What is the net change in $w$?

Consider a function $w=f(x,y,z)$. If $x$ increases by $1$ unit $w$ increases by $15$ units, if $y$ falls by $2$ units $w$ increases by $5$ units and if $z$ falls by $6$ units $w$ falls by $1$ unit. ...
2
votes
0answers
27 views

Exponents and order of execution [duplicate]

If presented the following, what order should the parentheses be added? 2^2^2^2 It seems most tools go right to left. Is that correct/expected? I could not find clear information on this. Thank you,...
0
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0answers
28 views

Trigonometry Angle Addition and Subtraction

I'm working on a problem. The problem is boxed in Blue. Ignore the right side boxed in green, it's unreleated. Inside the blue box, I have highlighted in green where my error is when solving this ...
1
vote
1answer
20 views

Sharing moving costs with housemates

My housemates and I just moved and we've got a few costs associated with it as well as a refund from our previous house. Who owes who what. There are three of us. We are receiving a refund of 848.08 ...
4
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0answers
57 views

Is there an infinity of $k \in \mathbb{N}$ s.t. $2 {k \choose k/2} - 1$ is prime?

my question is basically in the title. Is there a way to answer it, or are there any theorems or conjectures regarding it? Thank you.
1
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1answer
27 views

Adding the cardinals of not disjoint sets ( without inclusion of one set in the other) : does cardinal arithmetics offer a formula?

This question has been suggested to me by this post : How to prove that $|P(A)| + |P(B)| = 16$? Suppose A and B are disjoint. If I want to add the cardinal of P(A) and of P(B) , I cannot use this ...
0
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3answers
40 views

Why is raising to the 32nd power the obvious thing to do here?

I'm reading Don Knuth's "Selected Papers on Fun & Games" and early on there's a paper called "Representing numbers using only one 4". He does 64 and then starts to verify it like this $$64=\...
1
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3answers
50 views

Proof of X - (-A) = X + A. (Is it possible to prove?) [closed]

I have a problem with arithmetics. Is there is a proof that X - (-A) = X + A? Not just some analogy or "mind-trick". If so, could you tell me it or at least give some link or refer me somewhere? (may ...
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votes
1answer
42 views

contribution to the average

I'm calculating the conversion rate by employee. Employee1 got 2 new customers out of 8 that he was working with. Employee2 got 3 out of 6. Employee3 got 0 out of 2. Conversion rate of Employee1 ...
1
vote
1answer
94 views

$\,m = {\rm lcm}(a,b)\iff a,b\mid m\ \, \& \ \gcd(m/a,m/b)=1$

For $a \in\Bbb N$, $b\in\Bbb N$, $μ \in\Bbb N^*$, we have $μ = \operatorname{lcm}(a,b) \iff μ = αa\text{ and }μ= βb$ and $\gcd(α,β)$ is $1$ Till now I succeeded to prove the left $\Rightarrow$ ...
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votes
1answer
38 views

Calculation of digits [closed]

Suppose that an array of numbers from $1$ to $10^{23}$ is given. Let's calculate the sum of digits of each number. What kind of numbers among them are more with a $3$-digit sum or a $2$-digit sum? ...
0
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0answers
41 views

Weighted Division with more than one factors

Let's say I have 6,000 dollars and I want to divide them in 5 different companies. The logic thing is to devide the 2 amounts and find the money per company. Now let's say I have 3 characteristics for ...
1
vote
3answers
46 views

How would I rearrange this formula? [closed]

I have a project that I need an equation for, and it looks like this: $$W = \frac{V}{0.15} \times V$$ I need to rearrange the equation, so that V is the subject. So, in this situation here: $$\...
1
vote
1answer
32 views

How can I properly force this “object” to follow the indicated path

I'm working with drones and I want them to follow a path. This is the current behavior (black is the path, red is the drone): As you can see, it goes to the destination point (C), but it doesn't ...
3
votes
2answers
149 views

Plurality of arithmetics? Or absoluteness of arithmetical truths? (i. e. Are all mathematical truths actually conditional?)

The following assertion is attributed to Russell ( as a quote from Mysticism and logic) : Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is ...
2
votes
3answers
46 views

How to calculate the complex fractional values with sum of numbers and letters in an equation

Below is the equation. Not sure if I am doing the right thing but i can't seems to get the right value. $$ \mathbf{1.6\over 121.8} = \frac { \mathbf{15\over M}} {\frac{15} M + {250\over 78} } $$ ...
1
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1answer
20 views

How to transform a fraction into the integer that is in the denominator?

Suppose I have a function that has transformed a sequence of integers like so: $$ f(n) = \log_{10}\frac{1}{n} $$ I then want to convert those numbers back to $n$. I understand that I first must take ...
3
votes
2answers
41 views

Countability of a subset of sequences

Let $\mathcal{A} = \{a \in \{1,2,3,4,5\}^\Bbb N : |a_i- a_{i+1}| = 1 \; \forall i\}.$ Is the set $\mathcal{A}$ countable? I tried an argument like Cantor's diagonalization process but without success....