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.

4,746 questions
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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)
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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 ...
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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 ...
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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, ...
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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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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 ...
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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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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.
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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, ...
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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. ...
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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 ...
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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 ...
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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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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 $x$ ...
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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 ...
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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. ...
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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,...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 ...
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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. $$\mathbf{1.6\over 121.8} = \frac { \mathbf{15\over M}} {\frac{15} M + {250\over 78} }$$ ...
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 ...
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....