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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6
votes
1answer
64 views

“there exists” and “for some” are the same, right?

I think "there exists" and "for some" are the same, but still want to make sure. Ex: $x > ky$ for some k or there exists a k such that $x > ky$
0
votes
3answers
46 views

Arithmetic and geometric sequence

Which two numbers should be placed between -5 and 49 so that the first three numbers form an arithmetic sequence, whereas the last three numbers form a geometric sequence?
2
votes
1answer
23 views

Check algebraic transformation with trial numbers?

I did some algebraic transformations on equations with multiple real variables $x_i$, and I'd like to check whether the transformed equation is still valid. The equations are basically only rational ...
2
votes
2answers
32 views

Order of parsing + and -

This seems like an absurdly simply question, and is possibly below the level of this forum, but it seems the most sensible place. I'm building an arithmetic equation parser, and currently working on ...
10
votes
2answers
138 views

When is $\sqrt{a^2}=\pm a$ and when is $\sqrt{a^2}=a$?

When we derive some formula and have to do huge algebraic expansions that deal with raising powers we use exponent rules mindlessly and we never write down the $\pm$ symbol. Why is this right? My ...
-1
votes
2answers
107 views

2+2=square root of 16. What's the appropriate answer? [closed]

4? Positive and negative 4? I just got into an argument with a buddy about this. He argues if it's not an i, it's not included as a imaginary number, but only the real positive number.
0
votes
3answers
57 views

Exponential Function, Help Appreciated :-)

my text book asks me to 'Simplify, and express in terms of positive indices'. But my answer always seems to come up with: $x^{\frac {35} {36}}$. The term is $$\frac{ (x^{-\frac 1 2})^{\frac 2 3} \ x^{...
6
votes
1answer
81 views

Tzaloa 2015 game problem (piles with $1,2,4 \dots 2^{19}$ coins each)

We have $20$ piles with $1,2,4,8\dots 2^{19}$ coins repectively and two players. In each turn a player must select five piles that have at least one coin and remove exactly one coin from each. Player $...
1
vote
2answers
79 views

Combination of $n$ objects taken $p$ at a time where $n$ contains $r$, $s$, and $t$ identical objects.

I am talking about something like this: $ N = \{2, 3, 3, 3, 5, 5, 7\}$ $ n = 7$ $ s=3 $ $t=2$ In my case specifically, those numbers in $N$ are the prime factors of a number $Z$ repeated the number ...
2
votes
3answers
38 views

average of an inequality

what is the result of $<1 + <1$? ; $<1 + <1 = <2$? or <1 + <1 = <1? Now what is that number divided by 2? Either we have: <2 / 2 = <1 or <1 / 2 = <0.5
4
votes
1answer
71 views

If $(x^2+y^2+z^2)=2(x+z-1)$, then show that $x^3+y^3+z^3$ is constant and find its numeric value.

I am trying to solve this question, If $(x^2+y^2+z^2)=2(x+z-1)$, then show that $x^3+y^3+z^3$ is constant and find its numeric value. I've tried this, $$x^2-2x + z^2-2z + 2 + y^2 = 0$$ $$ (x-1)^...
25
votes
6answers
594 views

What would Gauss do in this case: adding $1+\frac12+\frac13+\frac14+ \dots +\frac1{100}$?

We all know the story related to Gauss that Gauss' class was asked to find the sum of the numbers from $1$ to $100$ as a "busy work" problem and and he came up with $5050$ in less than a minute. He ...
2
votes
0answers
68 views

Solving $-1=e^a-2e^{av}$ as part of a equation system

Problem Given $f_2(x)=e^{ax-b}+c$ with $x \in \left(0,1\right)$, I am trying to calculate the parameters $a,b,c$ in respect to the following constraints: $$ \begin{align} f_2(0) &= 0 \\ f_2(...
0
votes
0answers
23 views

Definition arithmetic progressions of any given length.

I have been studying erdős conjecture on arithmetic progressions for some time and have an interesting question for you : How do I strictly define "a set containing arithmetic progressions of any ...
1
vote
1answer
99 views

Number puzzle : “You can't determine my sum.”

Albert said to Bob, "I have two unequal positive integers; the smaller is at least 2; the larger is at most 25. I will only tell you their product." So he did. Later, Albert has forgotten the numbers ...
-7
votes
1answer
98 views

Does 0/0 = a new branch of numbers? Have I made a mistake in the equation? [duplicate]

So I thought... 0/0 = x... then 0 = x*0... then 0x = 0... then its technically possible to divide by 0 again 0x/0 = 0/0 ... since 0/0 = x and 0x/0 = 0/0.. then x = 0x/0 ... 0x = 0 ... x = 0/0 .....
2
votes
0answers
241 views

Comparing Large Exponents with different bases.

How to compare large exponents with different bases? Is there any way to roughly approximate their values? For example, sort the elements of list below based on their magnitude. $381600^{809197},...
-1
votes
2answers
55 views

calculating costs of manufacture [closed]

I apologize in advance if I'm asking this question in the wrong forum, but I'm having trouble with the Math, not the spreadsheet here. I'm calculating the cost per round of hand made ammunition, and ...
0
votes
2answers
57 views

Understanding A simple mathematical addition operation

I was just doing a simple maths operation: $s = 158 + 46 \times -1: \Rightarrow s = 112$ and $s = (158 + 46) \times -1:\Rightarrow s = -204$ In the latter case $158 + 48$ gets calculated first ...
4
votes
1answer
119 views

Infinite exponentiation $n^{n^{n^{…^n}}} \equiv m \pmod q$ , find m?

let $(n,q) \in \mathbb N^{*^2}$ I was wondering if it was possible to find a function $f_q$ such that : $f_q(n)=m$ where $m$ is such that $n^{n^{...^n}} \equiv m \mod q$ or at least an easy way to ...
0
votes
2answers
55 views

division of fraction simplification

The expression is this: ${{y^2 - y} \over 1 {}} \div {{y^2 - 1} \over 3}$ The first step is to swap the second expression round to: ${{y^2 - y} \over 1 {}} \div {3 \over {y^2 - 1}}$ The answer ...
4
votes
0answers
70 views

imo question to be explained in a manner so as to a layman

Suppose that you mark a finite collection of points on an infinite plane in such a way that you cannot draw a straight line through any three marked points. We define a windmill to be the following ...
2
votes
2answers
59 views

Proving that an expression returns a real non-integer number (Number 2)

Let $$a=443372888629441 = 17*31*41*43*89*97*167*331$$ $$b=(3+\sqrt{13})/2$$ $$c=(2+\sqrt{8})/2$$ $$d=(1+\sqrt{5})/2$$ How can you prove that the expression $$\frac{(b^a-1/b^a)-(c^a-1/c^a)-(d^a-1/d^...
0
votes
3answers
70 views

Proof of the division algorithm

I wasn't happy with the proof provided by the book, so I had an attempt at it, but I don't know if it's right. The theorem is: Let $a,b\in\mathbb{Z}$ and $b\neq0$. Then there exist unique $m,r\in\...
-1
votes
2answers
60 views

An Elementary Algebra (Ratios & Proportions) Problem

Let $a,b,c,d$ be positive real numbers in Continued Proportion (i.e., $\frac{a}{b} = \frac{b}{c} = \frac{c}{d}$), then show that $$d-a \ge 3(c-b).$$ or $$d -a = 3 + (some\ algebraic\ expression) $$
-1
votes
1answer
71 views

how many distinct number group possibilities exist in a powerball drawing if you exclude the powerball [closed]

in a powerball lottery draw you choose 5 numbers out of 59 with no repeating numbers how many distinct number groupings does this amount to is there an equation that can be used to calculate this?
0
votes
3answers
179 views

What is the value of $-(-6)$?

I know this is not absolute value, so what do the parentheses mean? If it was absolute value, it would have lines so I can rule that out. And I guess I should mention, the question I was asked is "...
5
votes
1answer
160 views

A beautiful book on arithmetic doesn't treat you like a little baby

The state of arithmetic today is disgusting. The textbooks on it are absolutely repelling, the authors treat it like a subject that will be of concern to only babies. They don't show any love, they ...
1
vote
1answer
45 views

Compound interest question

A property is mortgaged over $20$ years at an interest rate of $5.6$% per annum compounded annually. If the mortgage is £$120,000$, what are the annual repayments if payments are made at the end of ...
4
votes
5answers
2k views

If $x^3+y^3=72$ and $xy=8$ then find the value of $x-y$.

I recently came across a question, If $x^3+y^3=72$ and $xy=8$ then find the value of $(x-y)$. By trial and error I found that $x=4$ and $y=2$ satisfies both the conditions. But in general how ...
1
vote
2answers
2k views

Solving proportion problems involving three quantities

How do you solve proportion if 3 variables are given? I have looked in this site but i could not undertand it completely http://www.beatthegmat.com/ratio-proportion-3-variables-t34902.html 15 robots ...
0
votes
2answers
83 views

Arithmetic Sequence - Find the Last Number of Terms

The sequence is: $11, 13, 15, ... 59$ I need to find $i$ so that the sum of all terms before $i$ equals the sum of all terms after $i$ The simple way would be to calculate: $S_{i-1} = S_{n} - S_{i}$ ...
5
votes
4answers
159 views

How do I find the remainder of $4^0+4^1+4^2+4^3+ \cdots + 4^{40}$ divided by 17?

Recently I came across a question, Find the remainder of $4^0+4^1+4^2+4^3+ \cdots + 4^{40}$ divided by 17? At first I applied sum of G.P. formula but ended up with the expression $1\cdot \dfrac{...
0
votes
2answers
47 views

Take $\sqrt[n]{m}$ where $n$ is a positive non-integer number. Is this possible?

The title pretty much says it all. I am trying to figure out how to take the $n$-th root of a number $m$ where $n$ is a fractional number. Unfortunately all I could turn up on Google was how to take a ...
0
votes
3answers
93 views

If $ab(a+b)=2$ then what will be the value of $\frac{1}{(ab)^3}-a^3-b^3$?

The question given is, If $ab(a+b)=2$ then show that $\dfrac{1}{(ab)^3}-a^3-b^3=?$ $(a)\ \ \ \ \ 0$ $(b)\ \ \ \ \ 1$ $(c)\ \ \ \ \ 3$ $(d)-1$ I noted that $a=1$ and $b=1$ satisfy the ...
4
votes
2answers
54 views

Using alternate order of operations

Let's pretend, for a second, that we used PEASMD instead of PEMDAS. That is, addition/subtraction and multiplication/division are switched. Is it possible to write: $$(a\times b)+c$$ without ...
2
votes
1answer
305 views

How to calculate fuel cost and mpg?

A car has a mileage of "5 miles per litre" and traveled a distance of 573 miles. The cost of fuel is £1.09 per litre. How do I compute the miles per gallon(mpg) and the total cost of fuel for the ...
7
votes
3answers
719 views

Sums of Fourth Powers

While fooling around on my calculator I found: $$7^4 + 8^4 + (7 + 8)^4 = 2 * 13^4$$ $$11^4 + 24^4 + (11 + 24)^4 = 2 * 31^4$$ I'm intrigued but I can't explain why these two equations are true. Are ...
3
votes
2answers
57 views

How do we conclude that the relation is equal to $1$ ?

We have a curve of the form $$s^2-\alpha t^2=1 \tag 1$$ (in $ts$-coordinates). If $(a,b)$ and $(c,d)$ are points of $(1)$, then $(ac+\alpha cd, ad+bc)$ is point of $(1)$. $(a,b)$ is a point of $(1)...
1
vote
1answer
19 views

Logarithmically bounded function fulfills $f(n) \le \lceil m \cdot \log_b r \rceil$ for certain numbers $n,m,r$

Let $f : \mathbb N \to \mathbb N$ be a function such that $f(n) \le 1 + \log_b n$ for some base $b$ and all $n$. Now let $n \in \mathbb N$ have the property that $$ \frac{r^m - 1}{r-1} \le n < \...
24
votes
12answers
3k views

What is the accepted syntax for a negative number with an exponent?

A friend is taking a college algebra class and they are teaching him that $$-3^2 = -9$$ Their explanation is: $$-3^2 = -(3^2) = -9.$$ It has been a long time for me but I thought that in the ...
0
votes
1answer
40 views

Polynomials with range containing an arithmetic progression

Can I find a polynomial in a second degree in two variables from the values of which can be found an infinite arithmetic progression? Thank you!
1
vote
2answers
212 views

Binary expansion, finding the greatest power of $2$ less than a given number

I'm looking to better understand binary for a CS50 problem set. I'm not understanding transferring decimal notation to binary. For example, use 237. How to find the largest power of $2$ less than $...
1
vote
2answers
53 views

Show $n \cdot \log_b r + \log_b \frac{r}{r-1} \le \lceil n \cdot \log_b r \rceil$

Let $n$ be a natural number and $b, r > 1$ be two natural numbers, then I guess we have $$ n \cdot \log_b r + \log_b \frac{r}{r-1} \le \lceil n \cdot \log_b r \rceil. $$ where $\lceil x \rceil = \...
3
votes
2answers
70 views

A simple expression to map $\mathbb N^*$ bijectively to $\mathbb N$

Let $\mathbb N = \{ 1,2,3,\ldots \}$, then by the well-known "Cantor"-Scheme we have $\mathbb N \times \mathbb N \cong \mathbb N$. But even nicer is that we can write this scheme $\varphi : \mathbb N \...
-3
votes
3answers
78 views

How to calculate an elementary integral

How do you calculate $$\int\dfrac{2 du}{(u^2+1)^2}$$ It does not seem too difficult but I do not know which method to use.
1
vote
2answers
568 views

Given a time, calculate the angle between the hour and minute hands

I cannot understand the solution to the following programming problem. I will be very thankful for you help! Given a time, calculate the angle between the hour and minute hands Solution: • Angle ...
2
votes
1answer
75 views

Can you add a scalar to a matrix?

If I add a scalar to every element of a matrix, e.g. for a $2\times2$ matrix $$ \begin{pmatrix}a_{11} & a_{12} \\ a_{21} & a_{22}\end{pmatrix} + b \overset{?}{=} \begin{pmatrix}a_{11}+b & ...
0
votes
1answer
93 views

How to prove that $(a-b) \mod N = a \mod N + ((-b) \mod N)$?

I've gone through the similar post Modulo of a negative number . But that post is not about proof and I'm asking for the proof in general. This question is another follow up question of my previous ...
2
votes
1answer
56 views

Absolute value of infinite series sum

How does it come about that $$\left|\Sigma_{n=-N}^{N}c_n(f)e^{inx} - \Sigma_{-\infty}^{+\infty} c_n(f)e^{inx}\right| = \left|\Sigma_{|n|>N} c_n(f)e^{inx}\right|?$$ What happens with the $n$-index? ...