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
11 views

Clearing concepts for compound interest

A man banked $\$50,000$ into the bank which pays compound interest if $7.6\%$ per annum compounded every 3 months. The formula is $$ A = P \left( 1 + \frac r {100} \right)^n $$ where $P$ is the ...
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0answers
10 views

Confused between marked price , selling price , cost price

By selling an article at 20% discount off the marked price , a shop keeper still makes 10% profit on his cost . If cost price is $1200 , calculate the marked price of the article . I learned that ...
0
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1answer
27 views

Consecutive consecutive sums of equal value

Given the list of counting numbers, what is the largest amount of consecutive consecutive sums of equal value that can be found? Is there a limit? For example, [1, 2] and [3] are two consecutive ...
4
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0answers
53 views

Does this operation have a name?

For a field $F$, define the binary operation $\parallel :(F\mathbb{P}^1 \times F\mathbb{P}^1 \setminus\{(0,0)\}) \to F\mathbb{P}^1$ by $$a \parallel b = \frac{1}{\frac{1}{a} + \frac{1}{b}}.$$ This ...
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2answers
55 views

if $p\mid a$ and $p\mid b$ then $p\mid \gcd(a,b)$

I would like to prove the following property : $$\forall (p,a,b)\in\mathbb{Z}^{3} \quad p\mid a \mbox{ and } p\mid b \implies p\mid \gcd(a,b)$$ Knowing that : Definition Given two ...
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1answer
39 views

Understanding a proof of a corollary in chapter 2 about invertibility of a p-adic integer (Jean-Pierre Serre)

In a proof of a corollary in chapter 2, there is a step I don't understand. Corollary 2: Suppose $p \neq 2$. Let $f(X) = \sum_j a_{ij}X_iX_j$ with $a_{ij} = a_{ji}$ be a quadratic form with ...
2
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1answer
52 views

Determining a multiple of a power of 2.

I am thinking about this question which I believe is a possible GRE question. "Which of the following numbers is exactly divisible by 32? A) $1.9 \times 10^5 $ B) $1.9 \times 10^6$ C) $1.9 \times ...
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0answers
19 views

Help me out with this problem. [on hold]

If the income tax is increased by 19%, the net income is reduced by 1%. The rate of the income is?
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2answers
44 views

How to find value of $x?$

$A = x^{1/4} $ $B = x^{1/6}$ And $A^2 = 4B$ Find values of $x$ . Can I get a hint on how to solve this ?
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0answers
22 views

Computing $n^{\text{th}}$ root of a positive integer to arbitrary precision using integer arithmetic

There are various questions on this forum that appear similar, but my question pertains to writing code that can compute the $n^{\text{th}}$ root of a number $a$ correct to $p$ decimal places, where ...
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1answer
30 views

How to do 24.89 / 26.15 with long division?

How to do 24.89 / 26.15 with long division? Question is to find applied tax if 24.89 is pre-tax and 26.15 is post-tax. I'm aware of how to solve this with a calculator (1-(24.89/26.15))= ~.0482 = ~ ...
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0answers
23 views

Find the sum of all four digit numbers such that the number is the cube of the sum of its digits. [closed]

Find the sum of all four digit numbers such that the number is the cube of the sum of its digits.
4
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1answer
43 views

Fractions of powers of primes.

I'm wondering whether the following statement is true: Let $p$ and $q$ be two prime numbers (or more generally let $p$ and $q\neq 0$ be integers with $\gcd(p,q)=1$). Then for all $\varepsilon >0$ ...
1
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0answers
27 views

Unprovable identity over the integers

I was thinking about Tarski's problem, and was wondering what happens if we have a theory $T$ with two sorts $N,Z$ with intended interpretations $\def\nn{\mathbb{N}}$$\def\zz{\mathbb{Z}}$$\nn,\zz$ ...
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3answers
123 views

Why is the Fundamental Theorem of Arithmetic so important?

I've recently read about the Fundamental Theorem of Arithmetic and I think that I have just about understood the proof. What I found quite interesting at first was the "Fundamental" part in the name. ...
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3answers
26 views

Arithmetic progression. $a_3 + a_6 = -20$, $S_6 = -72$. Find $a_{11}$.

Arithmetic progression. $a_3 + a_6 = -20$, $S_6 = -72$. Find $a_{11}$. Formula for finding nth term is $a_n = a_1 + (n-1) * d$. Formula for finding sum is $S_n = \frac{a_1 + a_n}{2} * n$. I am ...
0
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1answer
19 views

time speed distance 2 [closed]

The Singhbad Express left Pune at noon sharp. Two hours later, the Deccan started from Pune in the same direction. The Deccan overtook the Singhbad Express at 8 pm. Find the average speed of the two ...
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1answer
24 views

Time Speed and Distance(train) [closed]

A train crosses a man travelling in another train in the opposite direction in 8 seconds.However,the train requires 25 seconds to cross the same man if the trains are travelling in the same ...
2
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1answer
34 views

Fraction simplification Rules

I am studying for GRE and One of the practice questions is a division. After converting my Mixed numeral I get 90/72 now I just have to simplify. What I understood is that you divide by Least common ...
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0answers
15 views

Term for “Remainder in the Whole”

If I have a proper fraction I want to know what the name is for the amount remaining in the whole. So given $\frac1 3$ I want the name of the term $\frac 2 3$.
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4answers
52 views

Is the 2011th term odd for this sequence and why so?

$a_n = a_{n-1} \cdot a_{n-2} + n$, $n\ge2$, $a_0 = 1$ and $a_1 = 1$. Is $a_{2011}$ odd. Why so? This is not a homework problem. I am appearing for an exam soon and I am solving sample questions for ...
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0answers
42 views

II. p-adic equations [2.1. Solutions] (J.-P. Serre)

Currently, I'm reading a chapter about p-adic equations in A Course in Arithmetic by Jean-Pierre Serre and I have a hard time understanding it. My questions/thoughts are in textboxes like these. ...
0
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2answers
42 views

Find the sum of this given expression… [closed]

$$1+(3+1)(3^2+1)(3^4+1)(3^8+1)(3^{16}+1)(3^{32}+1)$$
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0answers
65 views

Generators for a matrix group

Lets denote $\Gamma_0(4)$ the subgroup of $SL_2(\mathbb Z)$ : $$\Gamma_0(4):=\left\{\begin{pmatrix} a &b\\ 4c&d \end{pmatrix}\in SL_2(\mathbb Z)\right\}.$$ We also define $A$ and $B$ in ...
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1answer
30 views

Could multiplication be defined as $|A_1 \cup A_2 \cup ..A_n|$?

Taking discrete math which suddenly right now I am thinking of what dividing and multiplication do when it comes to what I learned in this class. But would multiplication be defined as the cardinality ...
1
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1answer
27 views

Numerical Analysis: Computer Arithmetic

I need to add, multiply fractions (i) Exactly using three-digit decimal arithmetic with chopping (ii) With three-digit arithmetic with rounding Say we had $$\frac{1}{6} + \frac{1}{10}$$ ...
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2answers
48 views

arithmetic problem concerning equilateral triangle

An equilateral triangle exists with vertices $(0,0), (a,11)$ and $(b,37)$. Using the distance formula three times, I eventually arrive to: $$a^2 + 121 = b^2 + 1369 = a^2 + b^2 - 2ab + 676$$ The only ...
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4answers
129 views

There does not exist any integer $m$ such that $3n^2+3n+7=m^3$

I have this really hard problem that I am working on and I just don't seem to get it. The question is: let $n$ be a positive integer; prove that there does not exist any integer $m$ such that ...
1
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1answer
27 views

Future Value and Present Value of a General Annuity Due

I understand that a general annuity due, the payments are made at the beginning of each payment period, and the compounding period is not equal to the payment period. Then to solve I need to transform ...
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1answer
21 views

How to Justify the way to solve “A / B * C”

this may be a silly (and duplicated or triplicated) question, but I don't know how justify one or other way to solve this: $A/B*C$ It is clear that: $(A/B)*C \neq A/(B*C)$ One I have heard some ...
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3answers
31 views

Arithmetic and proportions: cars in a garage [closed]

I am having trouble solving this problem: There are a total of 420 cars in a garage. They are in different colours. For every 2 white cars there are 3 black ones. For every 4 black cars there are 5 ...
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0answers
24 views

Exercise about radix

Anyone can help me with this problem? Find the integers that in decimal radix the tens and units of their square are equals. $a = 2p − 1, b = 2p + 1, c = 2p + 3.$ Find $p$ that $a^2 + b^2 + c^2$ is ...
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0answers
43 views

A question on ordinal arithmetic.

I have to order these two ordinals and I was just wondering if I have done it correctly. $\omega^\omega + \omega^3$ and $\omega + \omega^3 +\omega^\omega$ I have worked out that $\omega + \omega^3 ...
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1answer
19 views

Exercise fermat numbers

Someone can help me with this problem? $F_p=2^{2^p}+1$ Prove that for $2^n+1$ be prime, n have to be a power of 2. Prove that for $k\ge1$ $F_p \mid F_{p+k}-2$ Deduce that $F_p$ and $F_{p+k}$ are ...
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1answer
12 views

How to find the summation of phasors in exponential form

Is there any expression in form of $A e^{j\phi}$ for the following summation: $A_1 e^{j\phi_1} + A_2 e^{j\phi_2} + ... + A_n e^{j\phi_n}$?
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0answers
27 views

Understanding Fermats Little Theorem

Say I was told to find: $4^{1000} (mod 7)$ Since The modulo is prime, I can use fermats little theorem, now I'm just wondering if my steps are correct: We have that: $4^6 = 1(mod 7)$ //congruent ...
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2answers
35 views

Number of decimals to round to after division so that reversing the operation is precise

I'm dividing number A (positive, with up to 2 decimal places) by another number B (positive, up to 3 decimal places) to arrive at my result, C. I'd like to round C to the fewest decimal places so ...
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1answer
35 views

Calculate how much ethanol to add to petrol to get a desired blend

Take the following problem: Data: I have $20$ liters of petrol in a tank: Assume that e85 is defined as $85\%$ of ethanol and $15\%$ of petrol; Assume that petrol does not contain ...
1
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1answer
25 views

Given values of X , find fractions

Solve the equation expressing $x$ in terms of $y$ $$x^2 - 6xy + 5y^2 = 0$$ Given that area of part $A$ of a circle is $$3x^2 - 2xy - y^2 \text{ cm}^2$$ Area of circle is $4x^2$ cm^2 Calculate ...
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1answer
105 views

Find the sum of $1^{n}-2^{n}+3^{n}-4^{n}+\cdots+m^{n}$

After seing this question I started wondering about a generalization of a similar sum. The sum is $$ S(m,n)=\sum_{r=1}^{m}(-1)^{r-1}\;r^{n} $$ I gave this to WA to crunch and it gave $$ S(m,n)= ...
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4answers
29 views

Numbers question

A particular plant in the garden needs to be watered every 3 days , trimmed every 4 days and fertilised every 8 days . If a gardener performs these 3 tasks on Day 1, list the days that the gardener ...
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0answers
60 views

Pos properties.

Given $n\in\mathbb{N}$, and $f:\mathbb{N}^*\rightarrow \mathbb{N}$, let define $Pos$ as: $$Pos(f)(n)= |\{x \leq n, f(x)=f(n)\}|$$ When given $n\in\mathbb{N}$, this function gives the 'position' of ...
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2answers
23 views

Number patterns of fractions

I can't seem to find a difference for this number pattern .. Given a sequence ... $1, 2/3 , 4/7 , 8/15 , 16/31 ... $ What is the next term of the sequence ? I can't seem to spot a difference ...
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3answers
367 views

Prime numbers on a non-standard model

I can't imagine how this is possible: Let $\mathcal{M}$ be a nonstandard model of arithmetic. Show that: There is an element $a\in M$ such that for all prime numbers $p$, we have that $\mathcal{M} ...
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3answers
30 views

Prove that : $10^{5n+2}+(-1)^{n}\cdot 4 \equiv 0 \pmod {13}$

Prove that : $$10^{5n+2}+(-1)^{n}\cdot 4 \equiv 0 \pmod {13}$$ I don't have enough skills in modular to do it Please help
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0answers
24 views

What is the logic of priority of operations?

For example $2+2\times2$ is $6$ not $8$. Actually $+$ and $\times$ are binary operations on $\mathbb Z$. but here there is an triple $(2,2,2)$ which we sent to $2+2\times 2$. So we have to put and ...
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1answer
36 views

Mathematics- Time and work

A & B can complete a job in 8 days and B & C can do it in 12 days. A & B commence the work and do it for 4 days, then A leaves. B continues for 2 days and leave. C starts working and ...
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1answer
136 views

What is the definition of $n\cdot n\cdot n$?

Intuitively, What does it mean when you multiply numbers? I asked my professor about what does it mean when we multiply $5\cdot 5\cdot 5$. He said there is no definition of this thing in mathematics. ...
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0answers
22 views

Characterization of elementary arithmetic operators to explain certain properties in programming languages

In the LISP-like family of programming languages, the four elementary arithmetic operators behave differently: + and * can take ...
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5answers
81 views

How do I average two numbers that are already averaged?

$50$ juniors and seniors are tested. $35$ of them average $80%$. $15$ of them average $70%$. What is the average of the class of $50$? We tried $(70+80)/2$ but that was $75$ and the real answer is ...