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

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1answer
76 views

Which one of the following logical propositions is to be preferred?

I'm trying to update the symbolism of Giuseppe Peano's "Arithmetices Principia", to make the translation freely available. Might I ask you, which of the following might be a correct mathematical ...
5
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1answer
151 views

Time and distance: Police and a thief with a twist.

A thief was given a head-start of 15 hour. The velocity of the thief being 4 km/hr and the police chasing after him be 5 Km/hr. A dog is moving to and fro between the police and the thief, starting ...
0
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1answer
33 views

Tree addtion has to do with Pascal's Triangle, why?

Let me define tree addition of a list of numbers as follows: 4 3 2 1 7 5 3 12 8 20 I conjecture that it is true that the tree addition of n numbers ...
3
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3answers
70 views

Find the largest $k$ such that $3^k$ divides the product of the first $100$ odd integers

Let $P$ be the product of the first 100 positive odd integers. Find the largest integer $k$ such that $P$ is divisible by $3^k$. There are $50$ odd numbers and $50$ even numbers between $0$ and ...
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3answers
33 views

Complex values of the cube root

I just learned that the cube root has 2 complex roots. For example, the cube root of 8 has : 2 , -1 plus or minus square root of 3 *i I was wondering, how do you find those conjugate complex values ...
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2answers
40 views

simplifiying an expression $(n + 1)! − 1 + (n + 1) \cdot (n + 1)!$

I've been stuck on this one problem and I have a problem on the process simplifying this equation so that it is $(n + 2)! − 1.$ $$(n + 1)! − 1 + (n + 1) \cdot (n + 1)!$$ If anyone could shed some ...
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1answer
34 views

10% fraud, while purchasing and selling. Whats the overall profit?

Ok, so the answer i find logical is $21$%. Like : 100 bucks paid, 110 items got. (10% profit). Then, 110 items you sell at 10% profit, you get 121 items worth of bucks. So, 100 bucks investment, 121 ...
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5answers
145 views

Show that $2^{105} + 3^{105}$ is divisible by $7$

I know that $$\frac{(ak \pm 1)^n}{a}$$ gives remainder $a - 1$ is n is odd or $1$ is n is even. So, I wrote $ 2^{105} + 3^{105}$ as $8^{35} + 27^{35}$ and then as $(7\cdot 1+1)^{35} + (7\cdot ...
2
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3answers
56 views

Number in tens place

A number in tens place in result of $4^{2015} \cdot 9^{2016}$ is? Obviously without using calculator, though I doubt it could count with those high numbers. By tens place I mean, for example if you ...
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2answers
49 views

Number of boys in school

We have $400$ students in a school. Every $20^{th}$ student failed at the end of the school year. Which was $2\%$ of schools girls and $10\%$ of schools boys. The number of all boys attending the ...
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2answers
77 views

Number addition riddle

I got this math "riddle" in one of my math test, and I would love to know how to solve it. If $$S = 1 + 2 + 3 + 4 + \ldots + 2015,$$ then a sum of $$1 + 2 + 3 + \ldots + 2015 + 2016 + \ldots + 4030$$ ...
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1answer
59 views

Number of apples in a basket riddle

You have six baskets with apples - 10,12,15,20,22,25 (this is how many apples there were in them - 10 in first, 12 in second..). Some of the apples are red and some are green. After one basket was ...
0
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1answer
70 views

What is the difference between the largest and smallest possible positive roots?

I am faced with the following question: What is the difference between the largest and the smallest possible positive roots of $4x^5 + 3x^3 -5x^2 + 7x - 12$? Now, my first attempt was to try ...
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3answers
19 views

Is it possible to convert fraction to decimal using only addition and subtraction?

I am working on a programming challenge that requires me to implement addition, division, and modulo using only addition and subtraction. Cool, simple enough: ...
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3answers
82 views

Easy inequality going wrong

Question to solve: $$\frac{3}{x+1} + \frac{7}{x+2} \leq \frac{6}{x-1}$$ My method: $$\implies \frac{10x + 13}{(x+1)(x+2)} - \frac{6}{x-1} \leq 0$$ $$\implies \frac{4x^2 -15x-25}{(x-1)(x+1)(x+2)} ...
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2answers
64 views

Generalized formula for sum of products.

Q:The sum of all possible products of the first n natural numbers taken two by two is? I did not understand the question as it is.What exactly is being asked?I'd really appreciate an answer ...
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1answer
24 views

Find the kind of progression

The four positive numbers a,b,c,d are in arithmetic progression.What is the progression sequence of abc,abd,bcd? I found out the common difference b-a,c-b.. but that does not seem to be of much use.
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1answer
43 views

Number of the term

If the sum of n terms in AP is $3(n^2)+5$.What is the number of the term which equals $159$? My attempt: $3(n)^2-3(n-1)^2=159$.I got $n=27$ but the answer given is $21$.
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10answers
395 views

Prove that if $a,b \in \mathbb{R}$ and $|a-b|\lt 5$, then $|b|\lt|a|+5.$

I'm trying to prove that if $a,b \in \mathbb{R}$ and $|a-b|\lt 5$, then $|b|\lt|a|+5.$ I've first written down $-5\lt a-b \lt5$ and have tried to add different things from all sides of the ...
2
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3answers
34 views

Theory behind multiplying decimals

When multiplying two decimal numbers, you first ignore the decimals, find the product, then count the number of decimal places that need to be in the answer by taking the sum of the original decimal ...
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1answer
37 views

How to Normalize the Sum of Two Gaussians

I have the following function: $I(\theta_i) = I_0 + I_1\exp(\mu(\cos(\theta_i - \theta_s) - 1))$. Suppose I have two implementations of this function, whose parameters match with the exception of ...
3
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1answer
57 views

How do I find the sum of first N numbers common to 2 APs?

Here is the question - Certain numbers appear in both arithmetic progressions 17, 21, 25, ... and 16, 21, 26, ... . Find the sum of first 100 numbers appearing in both progressions. The ...
5
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1answer
70 views

Find prime numbers $p,q$ such that $p^n+p^{n-1}+…+p+1=q^2+q+1$

Let $p,q$ are prime numbers and $n$ is a even number such that : $p^n+p^{n-1}+...+p+1=q^2+q+1$ Find $p,q$? I think : $p^n+p^{n-1}+...+p+1=q^2+q+1\Rightarrow p^n+p^{n-1}+...+p=q(q+1)\Rightarrow ...
2
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1answer
59 views

Small integral representation as $x^2-2y^2$ in Pell's equation

Let $k$ be a "representable" positive integer, in the sense that $k=|x^2-2y^2|$ for some integers $x,y$. Does it necessarily follow that $k$ can also be represented with small parameters, i.e. ...
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1answer
24 views

Does using the syntax X%% make sense?

I know percentages can be multiplied, as they're basically just fractions, so it makes sense to ask what 50% of 72% of 10 is, for example. But would anybody use an expression like 3%% as shorthand for ...
3
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2answers
25 views

Calculating the value of numbers with different operations

Calculate the value of: $$-14 + 49 \times 21 - 63 + 56 \div 35 \div 28 \times 70 - 42 \div 7$$ I noticed the numbers are a factor of $7$, so I took out $7$ as a common factor: $$7[-2 + (7 \times 3) ...
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1answer
41 views

Simple Interest Problem Ambiguity in Conventions

I am solving some simple interest problems. Following questions are creating ambiguity with conventions, hope someone will clarify what is going on. In what time does sum of money become 4 times ...
3
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1answer
29 views

Significant figures during intermediate steps in a calculation

If I have some values to use in a calculation, which all have 3 significant digits, then I know that the result will also have no more than 3 significant digits. Am I allowed to round up/down to 3 ...
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1answer
108 views

What is the difference (or relationship) between geometric length and arithmetic numbers?

In Abbott's Understanding Analysis there was a phrase like, "Ancient Greeks did not understand the difference (or relationship) between geometric length and arithmetic numbers." What is this ...
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2answers
56 views

Multiplication problem.

What would be the value of z in this question? If $z=2,$ the relation becomes $22\cdot wx = 594,$ which gives $wx=27.$ Partial product of $22\cdot 27$ is $154 + 440.$ It's incongruous with the ...
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0answers
32 views

Arithmetic progressions in subset

Let $S$ be a subset of $\{1,\dots,n\}$. Does there exist a good algorithm to find a partition of $S$ into "reasonably long" arithmetic progressions? Many thanks!
2
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4answers
43 views

$10$ Distinct Integers from a set and their sum equals to $954$

$10$ distinct integers from the set $ \left \{1;2;...;100 \right \} $ are chosen such that their sum is $954$. What is the smallest of the $10$ integers? How do I start this question? I have no idea ...
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0answers
28 views

Calculate new least common denominator

A parcel (lot) has an area of $547$ with co-owners that own a certain share in factions: Person $1$ has $\frac{1}{8}$, Person $2$ has $\frac{1}{8}$, Person $3$ has $\frac{2}{8}$, Person $4$ has ...
2
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0answers
36 views

How to reduce exponentiation expressions?

It is a simple question but I am afraid of its simplicity. Is that correct : $2^{30}+2^{30}+2^{30}+2^{30} = 2^{30}(1 + 1 + 1 + 1) = (2^{30})\cdot 4 = 2^{30}\cdot2^2 = 2^{32}$? I am doing complex ...
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1answer
76 views

How to find the nth term of this sequence?

How do I find the $n^{th}$ term, and what is it? $$ 1, \dfrac{1}{4}, \dfrac{1}{9}, \dfrac{1}{16}, \dfrac{1}{25},\dots$$ I mean I want to find out the relation how $n^{th}$ term depends on $n$. I'm ...
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1answer
67 views

Why is 0*0 is termed as indeterminate? [closed]

Why is 0 multiplied by 0 is termed as indeterminate? My idea about division by 0 is clear but not in the case of multiplication. Please help me by solving the equation : 0*0=indeterminate
2
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1answer
46 views

How to get the amount of digits after the decimal point

How can I easily find the amount of digits after the decimal point? For example: ...
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6answers
124 views

8 / 4 (4-2) = ? What is answer? [duplicate]

What is answer for 8 / 4 (4-2) = ? My answer is 4. But some says it's 1. And arguing each others. They even using some calculators for prove them. Even those calculators showing both 1 and 4 as ...
6
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3answers
78 views

Simplify $\left(\sqrt{\left(\sqrt{2} - \frac{3}{2}\right)^2} - \sqrt[3]{\left(1 - \sqrt{2}\right)^3}\right)^2$

I was trying to solve this square root problem, but I seem not to understand some basics. Here is the problem. $$\Bigg(\sqrt{\bigg(\sqrt{2} - \frac{3}{2}\bigg)^2} - \sqrt[3]{\bigg(1 - ...
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0answers
21 views

Arithmetic picard rank of smooth cubic surfaces

Assume a smooth cubic surface is defined over a field $k$ characteristic $0$, that it has line defined over $k$ and that its arithmetic Picard rank over $k$ is maximal i.e. $7$. Does this imply that ...
2
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3answers
38 views

How to calculate value of expressions when $a = 22$

$a = 22$ Round the answer to three significant figures: $\dfrac{77}{3a}$ for this one I am not sure if I do $\dfrac{77}{3(22)} = 1.17$ or $\dfrac{77}{3(22)} = 56$. Sorry if this is written in a ...
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2answers
18 views

Don't understand adding a system of compound inequalities

I'm reading a proof of the Division Theorem and one line that comes up is Since 0 ≤ r1 < b and 0 ≤ r2 < b , we have −b < r1 − r2 < b. I do not ...
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1answer
33 views

First 10 digits of large sum

There is a debate about this Project Euler problem in the discussion thread for the problem. The debate is whether you only have to add the first 12 digits of each number in order to get the answer. ...
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2answers
40 views

How to make a value scale with a probability?

Say I have a 50/50 chance to win/lose, and I have another value which is strength which starts at 0 but rises up by 5 every win to a max of 95. And every 5 strength ups my odds to win up to 95/100. I ...
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0answers
11 views

An inequality related to Brun's sieve

My question is about the presentation of Brun's sieve by Gelfond & Linnik's Elementary methods in the analytic theory of numbers. The authors denote by $P(\Delta~;~D~;~x~;~a_1p_1b_1, \ldots, ...
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5answers
73 views

Is it possible to split a division problem into parts, like in multiplication?

In multiplication we can mentally split a problem that is too big into multiple problems. For example: 26 * 40 = (20 * 40) + (6 * 40) = 800 + 240 = 1040 This is a very quick way to multiply ...
3
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2answers
60 views

Find prime numbers $p,q$ such that: $pq| p^p+q^q+1$

Le $p,q$ be prime numbers such that: $pq| p^p+q^q+1$ Find $p,q$ I don't have any ideas about this problem :( Thanks :)
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0answers
16 views

How to analytically find these rounding issues

Let's say we have a fixed yearly amount that we have to divide equally among an amount of days. For instance for $1,600 we may have: ...
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1answer
27 views

Calculate ideal value from graph

I have a question to ask, but before I do, let me just tell you that this might be a trivial - or even downright silly question. I only have a basic understanding of math, so please do try to keep ...
2
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0answers
36 views

The smallest prime factor with a set of digits

I was wondering if there was a way to logically/mathematically derive what the smallest possible largest prime factor to a number was, using each of the digits 1-9 only once. An example could be ...