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

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2
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2answers
35 views

Timeline if 0.5 millimetres= 1.5 years how many millimetres would equal 1 year

Hi I am working on a timeline and know that 0.5 millimetres equals 1.5 years how many millimetres would equal a year thanks.
0
votes
1answer
31 views

Why is $\left(1-\frac{1}{k}\right)^t < e^{-t/k}$?

I came across this statement, but can't see why it holds: $\left(1-\frac{1}{k}\right)^t < e^{-t/k}$ I'm sure it's something simple, but I don't have a great deal of mathematical experience. I ...
0
votes
2answers
17 views

Know total amount. Must divide in two parts so that one part is 10% from another part.

I know total amount. Must divide the total amount in two parts. Smaller part (amount) is 10% of bigger part (amount) so that smaller part plus bigger part is total amount. So total is 17091.54 ...
0
votes
1answer
14 views

proof of uniqueness (hint) $f(m,n)=n+1$ only if $n \ge m$

I'm a bit confused about this proof. let define on $\Bbb N$ a binary fucntion $f$ that satisfies (1) $f(m,n)=n+1$ if $n \ge m$ and (2) $f$ is commutative if I write the values of $f$ in a 2x2 ...
0
votes
2answers
71 views

Logic and mathematical variables as objects

I am currently working on describing a predicate logic for which the objects are mathematical variables. Thus I can say stuff like: $\forall x: R(x) \implies \text{operator}(x)=1$ Here $x$ is a ...
0
votes
3answers
72 views

How do I add multiple binary numbers without using a partial sum?

I know how to add binary numbers but what I normally do is add the first 2 binary numbers and then add the 3rd one to their sum. It is really slow. $$ 111_2 + 111_2 + 111_2 + 111_2 $$ Here is ...
5
votes
1answer
59 views

Halmos on Definability and Luzin on Division by 0

For a successful introduction of a new symbol (e.g. '$\emptyset$') into a mathematical discourse it is necessary and sufficient that the symbol refer to something (e.g. Existence + Specification in ...
0
votes
1answer
27 views

Confused by step in an inductive proof of arithmetical progression

In the book "What is Mathematics?" there is a section that provides an inductive proof of the arithmetic progression. Part of this proof is: $\frac{r(r+1)+2(r+1)}{2}=\frac{(r+1)(r+2)}{2}$ I don't ...
1
vote
1answer
38 views

Why does $ \frac {a}{b}$ of $c$ means $ \frac {a}{b} \cdot c$ [closed]

Why does it multiply when the preposition "of" appears?
0
votes
0answers
47 views

binomial coefficient as perfect powers

Bonjour to everyone. Let m be an integer. For: $ r \geq 2 \quad and \quad 4 \leq k \leq n-4, $ we know, as a consequence of the Sylvester theorem, that: $ {n \choose k}=m^r \quad (n \geq 2k) $ has ...
0
votes
1answer
45 views

Is there a way to simplify this equation?

$$ A = \left( 4000 \left( 1+\frac{x}{y} \right) \right)^4 \cdot \left( 1 + \frac{x+0.002}{y} \right)^4 \cdot \left(1+\frac{x+0.002+0.002}{y} \right)^4 $$
0
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0answers
30 views

Binary division algorithm

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2
votes
1answer
34 views

Prove that there are an infinity of prime $ak+b$, $a$ and $b$ coprimes

We have to integers $a,b$. I need to show that if $a$ and $b$ are coprimes then the set of prime numbers of kind $ak+b$ is infinite. How could I show it ? I know how to do that for $4k+3$ or $4k+1$, ...
0
votes
2answers
39 views

How do you get from this to this formula?

I have the formula : $$3×4^{n-1}×1×\left({1\over 3}\right)^{n-1}$$ And I would like to know how to get to this one (which is equal) : $$3× \left({4\over 3}\right)^{n-1}$$ How can I do that ?
0
votes
0answers
44 views

What is the smallest division without a fraction?

Is there a mathematical formula to calculate the smallest division of a fraction with both numbers not being a division? I'm not a mathematician (and not English), so I hope I use the correct terms. ...
-2
votes
2answers
29 views

arithmetic series problem

if $S(n)$ is a function representing the sum of an arithmetic series, determine the series with $S(13) = 507$ and $S(25) = 2025$ oh and the answer is supposed to be $$S(n) = \frac{7}{2}n^2 - ...
6
votes
1answer
402 views

What is a simple way of computing the following fraction?

Compute the value of the expression: $$\frac{(10^4+324)(22^4+324)(34^4+324)(46^4+324)(58^4+324)}{(4^4+324)(16^4+324)(28^4+324)(40^4+324)(52^4+324)}$$
1
vote
1answer
17 views

How to determine operantors between given numbers to get a given result

In a children's math book I found the following example: There are $2$ numbers: $242, 961$. You can use these numbers as many times as you want, and you can use any arithmetical operator ...
1
vote
1answer
24 views

Normalisation of $\mathbb{Z}$ in $\mathbb{Q}(\sqrt{d})$ is UFD…

We know that the normalisation of $\mathbb{Z}$ in $\mathbb{Q}(\sqrt{d})$ where $d\in \mathbb{Z}$ is $$O=\mathbb{Z}[\beta], \text{$\beta=\sqrt{d}$ if $d\equiv2,3 \pmod 4$}; \ \frac{1+\sqrt{d}}{2} ...
15
votes
3answers
397 views

About an inequality including arithmetic mean, geometric mean and harmonic mean

For any $n$ positive real numbers $a_i\ (i=1,2,\cdots,n)$, let us define $A,G,H$ as $$A=\frac{\sum_{i=1}^{n}a_i}{n},\ G=\sqrt[n]{\prod_{i=1}^{n}a_i},\ H=\frac{n}{\sum_{i=1}^{n}\frac{1}{a_i}}.$$ ...
1
vote
2answers
52 views

Word for the number being added-to OR subtracted-from another number

I first asked this on english.stackexchange.com, but this site would probably be a better-suited to answer it: In division, we have a dividend and a divisor. According to this page, we also ...
3
votes
0answers
57 views

Sum of Gauss sum

Let $p$ be an odd prime, $v \in \mathbb{N}$ be a positive integer, and $c\in \mathbb{Z}$. Set \begin{align} G(c,p^v):=\sum_{\substack{d \bmod p^v \\ (d,p^v)=1}}{ \left(\frac{d}{p^v}\right) {e}^{ { ...
1
vote
3answers
54 views

Inequality involving conjugate numerator/denominator pairs

Question is to solve: $$\frac{(x-2)(x-4)(x-7)}{(x+2)(x+4)(x+7)} > 1$$ I thought I could negate terms to make them equal (i.e. $-(x-2)$), but that does not happen. I could subtract $1$ from ...
0
votes
1answer
14 views

How to add up multiple intervals and check if they complete a known interval?

If my initial/known interval is [0,20) or length 19 And the 3 intervals are: [0,5), ...
-1
votes
2answers
78 views

Why Can't We Divide by Zero? [duplicate]

It always seemed to me any number X divided by zero would simply be X, since we're dividing by nothing, so then the original number wouldn't be altered. Why isn't this true? Can this ever be true?
0
votes
2answers
26 views

Divisibility Problem: How can I solve this?

Suppose that $a,b,q,r$ are any integers such that $b > 0$ and $a = bq + r$, with $0\le r<b$, and suppose $b|a$. Must it be the case that $r = 0$? Justify your answer. Can anyone please let me ...
2
votes
3answers
45 views

Solving this inequality

Question: Solve: $$\frac{5x-6}{x+6}<1$$ My attempt: $$\frac{5x-6-x-6}{x+6}<0$$ $$\Rightarrow \frac{4x-12}{x+6}<0$$ $$\Rightarrow \frac{x-3}{x+6}<0$$ $$\Rightarrow (x-3)(x+6) < ...
2
votes
4answers
257 views

How do you work out $\sqrt[4]{16^3}$ without a calculator.

$$\sqrt[4]{16^3}$$ I just don't know what to do when I get to $4096$. The original equation was $16^{3/4}$.
1
vote
2answers
56 views

Isn't this wrong?

This worksheet This question: $$w^2 - w \leq 0$$ This answer: $$(-\infty, -1] \cup [0, 1]$$ Isn't this wrong ? At $w = -2$, it becomes: $(-2)^2 - (-2)$, which is $4 + 2$, which is $\geq 0$. But ...
1
vote
3answers
42 views

How to solve this inequality question without manual checking?

Question: Find the maximum integral value which satisfies: $$\frac{x-2}{x^2-9}<0$$ I know that this means either of the following: #1. $x-2<0$ and $x^2-9>0$. Implies that $x \in (3, ...
1
vote
6answers
164 views

Why does $\frac{4}{2} = \frac{2}{1}$?

I take for granted that $\frac{4}{2} = \frac{2}{1}$. Today, I thought about why it must be the case. My best answers amounted to $\frac{4}{2}=2$ and $\frac{2}{1}=2$; therefore ...
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votes
2answers
34 views

In a lottery 5% of the tickets printed can be redeemed for prizes [closed]

In a lottery $5$% of the tickets printed can be redeemed for prizes and $5$% of those tickets have values in excess of $TK.50$ .IF $6000$ tickets were printed how many of them can be redeemed for more ...
2
votes
1answer
70 views

Prove this simple arithmetic relation

Prove that if $$a \mid b$$ and $$a \mid c$$ then $$a \mid bx+cy$$ for any integers $x$ and $y$. Here's my proof: $$b = ak$$ $$c = am$$ $$bx+cy = akx+amy = a(kx+my)$$ Notice that $kx+my$ is an ...
3
votes
3answers
240 views

Which is greater: $1000^{1000}$ or $1001^{999}$

Question: Find the greater number: $1000^{1000}$ or $1001^{999}$ My Attempt: I know that: $(a+b)^n \geq a^n + a^{n-1}bn$. Thus, $(1+999)^{1000} \geq 999001$ And $(1+1000)^{999} \geq ...
1
vote
3answers
38 views

Generate numbers that add up to X

I have isolated the algorithm of a keygenme, but I am running into difficulty with creating the keygen. The key has a length of seven digits, and the sum of each of the digits in the key must be ...
3
votes
1answer
43 views

Prove the sequences $\lfloor \alpha n\rfloor $ and $\lfloor \beta n\rfloor $ are disjoint

Here is another problem from a problem set that I can't solve. Let $\alpha$ and $\beta$ be irrational positive numbers such that $\frac{1}{\alpha}+\frac{1}{\beta}=1$ Prove that the sets $\{ ...
2
votes
5answers
83 views

How much zeros has the number $1000!$ at the end?

I know that it depends of the factors of five and two. But the number is too long to figure how much factos of five and two there are. Any hints?
6
votes
0answers
121 views

Solution of $\large\binom{x}{n}+\binom{y}{n}=\binom{z}{n}$ with $n\geq 3$

I found this question in an old problem set. There's no hint or solution mentioned. For $n \geq 3$, prove or disprove the existence of $(x,y,z) \in \mathbb N^3, ...
2
votes
2answers
151 views

The number $25!$ has exactly 7 trailing zeros, true or false?

I don't know how to determine it... any hints?
0
votes
2answers
33 views

Solving two systems with two unknown?

Let's say if we are giving the following two equations: $$ 1= X/(X^2 +Y^2) $$ $$ 2= Y/(X^2 +Y^2) $$ How are we going to solve for X and Y [ by HAND ] ? Why would Summing the squares of the two ...
1
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1answer
49 views

If $p=1\cdot 3 \cdot 5 \cdot 7 \cdot 9 \cdot … \cdot 2011$, then the units digit of $p$ is five

I know there is a $5$ on the sequence, but i don't know how and why his presence leads to the final units digit of the product.
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vote
1answer
35 views

My small theory…

It is given that 'a,b,c' are whole nos. Now 'a' is an odd no. while 'b' is an even no. Prove that:- a/b + c = x where 'x' is a fraction, equal to 'n/d' where n is an odd no. and d is an even no. and ...
2
votes
0answers
155 views

Relationship between two elements of two matrices with two numbers are not elements of the two matrices

I have two matrices, $$A= \left[ \begin{matrix} 5 & 10 & 15 & \cdots \\ 17 & 28 & 39 & \cdots \\ 35 & 52 & 69 & \cdots \\ \vdots & \vdots & \vdots & ...
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0answers
21 views

Determine an arithmetic relation

Let $f$ be an arithmetic function. Let $p$ be a prime number, $\chi(n)=\left(\frac{n}{p}\right)$ be a primitive Dirichlet character modulo p, where here $~\left(\frac{n}{p}\right)$ is the ...
3
votes
1answer
67 views

The function $f(t)=2+\sin(t)+\sin(t\sqrt2)$

The function $f$ defined on $\mathbb{R}$ by $$f(t)=2+\sin(t)+\sin(t\sqrt2)$$ can never reach $0$. Can we find some sequence $(t_n)_{n\geq0}$ such that $$\lim_{n \to \infty}f(t_n)=0 \ \ \ ?$$ Or in ...
0
votes
2answers
55 views

Does $\frac{8k-1}{4}$ belongs to $\mathbb{Z}$?

Does $\frac{8k-1}{4}$ belongs to $\mathbb{Z}$ for some $k\in \mathbb{Z}$ ? or we can prove that this never belongs to $\mathbb{Z}$ ?
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votes
2answers
55 views

Rigorous proof for the following [closed]

Please give a rigorous proof: For all $A, B$ $$(1/A)(1/B)=1/(AB).$$
1
vote
1answer
65 views

Grade School Math: Bad math, or new meanings?

I came across this online quiz discussing the new Common Core education standards, and it all seemed pretty reasonable, until I came across this question: In the number below, how many times ...
1
vote
1answer
20 views

Comparing powers with different bases without logarithms

I want to compare : $17^{31}$ and $31^{17}$ , this is a solution but I want another one and without using logarithms, only using the fact that $17=16+1=(2^4)+1$ and $31=(2^5)-1$ how could it ...
0
votes
1answer
28 views

Can we define the equality as $a=b$ iff $\frac{a}{b}=1$?

Well, The title i guess is enough to get what i'm looking for: I'm wondering if we can define equality of let's say $a$ and $b$ that the devision of $a$ over $b$ or $b$ over $a$ is $1$ : $$a=b ...