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

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0
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2answers
20 views

How to show that bound?

How to show that $\prod\limits_{i=1}^k \dfrac{k+i}{4i}$ is less than or equal to $1/2$ for all $k \ge 1$ Integer. I coulden't understand the answer in How to prove the bound on the probability?
1
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1answer
19 views

Multiplying game strategy

Given the following game, what is the strategy to win? Given $X,N\in \mathbb{N}$ such that $N>X$ and $N>1000$, two players play against each other. Each player multiply $X$ by $2$ or by $3$ by ...
2
votes
2answers
69 views

A positive integer $n$ is such that $1-2x+3x^2-4x^3+5x^4-…-2014x^{2013}+nx^{2014}$ has at least one integer solution. Find $n$.

A positive integer $n$ is such that $$1-2x+3x^2-4x^3+5x^4-...-2014x^{2013}+nx^{2014}$$ has at least one integer solution. Find $n$.
3
votes
1answer
67 views

Are there non-equivalent cardinal arithmetics?

‎Generalizing a concept in mathematics is always a problematic situation. In most cases there are several ways to generalize a notion and it is not easy to decide if a particular generalization is ...
0
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1answer
17 views

Discount to a Negative number [on hold]

How do you correctly apply a 5% discount to -$1.00? Would you use 0.05% or -0.05%?
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0answers
47 views

Combining 2 numbers into a uniqe number

I am stumped on a problem, I have a set of numbers (lets say 2 numbers) A and B and i want to combine them into a unique number C where C is not reproducible by any other set thats not identical ...
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0answers
66 views

P=NP and human thought [on hold]

I've been thinking about P=NP a lot, and wonder if there could be a new type of math created - like 23 would equal two plus three, two minus three, two times three, and two divided by three, etc. So ...
0
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1answer
26 views

Does Conversion rates affect the profit earned?

About 100 USD were given to me as an initial investment. I converted them to INR and traded with it in buying stocks and also selling stocks. I am now left with say 6000 RS today. As all of you are ...
0
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2answers
17 views

GCD proof using fundamental theorem of arithmetic

prove: $\gcd(m,n)=1$ if and only if $\gcd(m^i,n^r)=1$ I believe you need to do something with fundamental theorem of arithmetic to prove one of the sides. Not quite sure though. Help is appreciated. ...
1
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1answer
42 views

Maximal number of colours in a palette that allows for fewer than 500 mixtures

An artist is planning on mixing together any number of different colours from her palette. A mixture results as long as the artist combines at least two colours. If the number of possible mixtures is ...
1
vote
1answer
14 views

Deriving Simple Interest from given compound interest of 3 years.

Here's my problem : If the compound interest on a sum of money for 3 yr at the rate of 5% per annum is Rs 252.20, the simple interest on the same sum at the same rate and for the same time is ? Can ...
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0answers
20 views

BODMAS Order of operations

9÷3(6×4÷8) Here we all can apply BODMAS and solve the equation in parenthesis first giving us 3. But after this step shall we solve by 9÷3(3) = 9÷9 = 1 or 9÷3×3 = 3×3 = 9 . Please help
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2answers
91 views

Multiplying a infinite number with a rational number? [duplicate]

Please do not down vote this question. It may be stupid, but I wonder. Why is it that we cannot multiply $3.99999\cdots$ by $4$ and write $16,....$?
0
votes
1answer
16 views

finding number in the boxes

Anne writes a list of numbers with sum of digits equal to 7 only and put 7 in the first box, 16 in the second box and 25 in the third box, and so on. What is the number in the 100th box?
0
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0answers
17 views

what is the loss percentage in selling the second horse?

If a man sell his two horse \rupee $4000$ each, he gets no profit and no loss. Suppose he sells one horse at $25$% profit, what is the loss percentage in selling the second horse?
0
votes
1answer
26 views

Solve denominator so quotient is whole number?

I have a simple equation. road_length = ROADLENGTH / ROADSPACING The problem is, I really need road_length to be a whole number because it's used in FOR loop in ...
0
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0answers
20 views

How can I teach a $7^\text{th}$ grade student the concept of ratio and proportion

How can I teach a $7^\text{th}$ grade student the concept of ratio and proportion with the use of teaching aids ( such as models or Charts) . One of my friends asked me this question. One possible ...
0
votes
2answers
16 views

Prime Factorizations that divide each other

Let n have prime factorization n = p^s1 · p^s2 · · · p^sk and let m have prime factorization m = q^t1 · q^t2 · · · q^tl If n|m, what must be true about the corresponding lists of primes and the ...
0
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1answer
24 views

What are the general solutions of the Diophantine equation $ ax+by+cxy+d=0 $

Does the diophantine equation $$ ax+by+cxy+d=0 $$ always have solutions ?
0
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1answer
60 views

What am I doing wrrong here that violates the rule that “order doesn't matter when multiplying and dividing?”

5 / 1 * 4 if I do the 5/1 first: (5 / 1) * 4 = 5 * 4 = 20 (final answer is 20) if I do the 1 * 4 first: 5/ (1 * 4) = 5/4 (final answer is 5/4) What am I doing wrong?
5
votes
2answers
105 views

$(-32)^{\frac{2}{10}}\neq(-32)^{\frac{1}{5}}$?

Is exponentiation by rational numbers defined only for simple fractions? $(-32)^{\frac{2}{10}}=\sqrt[10]{(-32)^2}=\sqrt[10]{1024}=\pm2$ (and $8$ other complex roots) ...
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2answers
25 views

Find sum of arithmetic progression [closed]

I have been given that A4(the fourth element) is equal to 5 and I have to find the sum of the first 7 elements. I tried using system to find A1(the first element) or d(the difference) but I was unable ...
1
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0answers
33 views

dividing polynomials using long division

I'm not following logic of using long division on polynomials. If you are using regular long division, we would do the following: ...
0
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1answer
23 views

I have problem solving this system

I have given arithmetic progression and I know that: the sum of the first element(A1) and the fifth element(A5) is equal to 18 A1+ A5 = 18 and that the sum of ...
0
votes
2answers
36 views

Will the Russian Peasant work with anything other than base 2?

The Russian peasant method involves doubling and halving by 2. Therefore you will get exact remainders of either 1 or 0, which perfectly represents one of the multiplicands in binary form. I just ...
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4answers
50 views

Approximate to whole number without calculator

Approximate this number to the nearest whole number without a calculator: $2^{\sqrt{5}}$ I don't know how to do this problem. Can you help me? My answer key says $5$. Also, how do I approximate ...
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votes
0answers
18 views

Solve: Multiplication and Division Equation.

Three-fourths of the students who are in Honor's Algebra are eighth-graders. There are 21 eighth-graders in the class. How many total students are participating in Honour's Algebra?
3
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1answer
49 views

“Alternating” sums of fourth powers.

Problem: Show that any integer $n$ can be written as: $$n = \sum_{k = 0}^N \epsilon_k k^4$$ where $N$ is a nonnegative integer and $\epsilon_k$ is in $\{\pm 1\}$ for every $k\leq N$.
3
votes
1answer
52 views

Finding lowest possible value

please help me with this problem: Find the lowest possible value of $$ x+y^3 $$ where both x and y are positive and x*y=1. I know how to solve this one using my method, but I was suggested to use ...
0
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0answers
25 views

What values will make this expression real [duplicate]

For what values of $z$ , where $z ∈ C$, will make the expression, $(iz - 1)$$/$$(z-i)$, real? So far, I've noted that if the expression, let's name it $w$, is real, then $w$ is equal to its ...
2
votes
5answers
330 views

Seeking elegant proof why 0 divided by 0 does not equal 1

Several years ago I was bored and so for amusement I wrote out a proof that $\dfrac00$ does not equal $1$. I began by assuming that $\dfrac00$ does equal $1$ and then was eventually able to deduce ...
2
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1answer
36 views

computing $29^{25}$ (mod 11)

I'm trying to learn how to use Fermat's Little Theorem. $29=2\cdot11+7 \Rightarrow 11\nmid29$ by the theorem we have $29^{10}\equiv 1$(mod 11) $25=10\cdot 2 + 5$ $ ...
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0answers
31 views

Number Pyramid Help

I was searching around the internet to try to find the name to the following pyramid: ...
5
votes
2answers
57 views

Intuition behind sum of multiplication arithmetic sequence

Maybe this is a stupid question but please guide and enlighten me patiently. I have just known something fact that quite shocking me. Let start from this simple fact $$\sum_{k=1}^n ...
0
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0answers
13 views

understand problem for limiting sum of a geometric progression

a more mathematically enlightened philanthropist endows a bursary that is to pay 100 000 to a student each year beginning now. The philanthropist is able to invest funds for the endowment at 10% p.a. ...
5
votes
1answer
64 views

Why did Frank Drake choose these math equations for the Voyager Golden Record?

Not sure this belongs in this or some other community, but one of the images on the golden record is a brief snapshot of our decimal system and then a few math examples. Here is the image in question: ...
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6answers
61 views

Positive integers $x$,$y$,$z$

If $x$ , $y$ and $z$ are positive integers and $3x = 4y = 7z$, then calculate the smallest possible value for $x+y+z$. How do you do this? Can someone please give me a hint?
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5answers
85 views

How can we derive the formula for sum of odd numbers?

We know that $\sum^n_{k=1}(2k-1)=n^2$. Can it be shown using AP?
6
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0answers
99 views

Mersenne primes

A Mersenne prime is a prime number of the form $2^p-1$ where $p$ has to be a prime number. Now, let $p_0$ be a prime number, and let us define the sequence $p_n = 2^{p_{n-1}}-1$. Is there a $p_0$ such ...
1
vote
2answers
27 views

Help me evaluate this equation in Scientific Notation

How do i solve this using Scientific Notation? $$ \frac{3\times 10^8}{4\times 10^{-5}} $$ I have been trying for hours now! Help please
19
votes
6answers
2k views

Subtracting Quarters of Squares Equals Multiply?!

Can anyone explain to me how/why this works (hopefully in mostly layman's terms)? It seems pretty magical to me at the moment. $${{(a+b)^2\over4} - {(a-b)^2\over4}} = a b.$$
0
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1answer
32 views

How can the two basic binary operations (addition and subtraction) be defined in set-theoretical terms?

I recently stumbled upon this interesting definition of mathematics: Math is the study of things that can be described as sets I am aware that the integers and the real numbers can be defined in ...
1
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1answer
33 views

Even powers and perfect squares

Does $2^{2k}$ (where $k$ is a natural number) always result in perfect squares?If so, why?I just tried it with a few values and it appears to be true. I need the result for this to simplify a ...
0
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1answer
28 views

Unique Number Calculations

What do you call numbers you can add together that will always be unique. a = 1, b = 2, c = 4 Any combination of the above will always result in a unique number. eg: 7 = abc, 6 = bc, 3 = ab Sorry if ...
4
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0answers
49 views

Prove $\forall n\in\mathbb{N}, \exists m\in\mathbb{N}; n=\pm1^2\pm2^2\pm\cdots\pm m^2.$

And we choose the positive and negative signs in a way that the equation becomes true. I think it can be proved with mathematical induction. So here's how I begin: For $n=1$, $1=+1^2$ which is true. ...
0
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2answers
68 views

Prove square root unde square root irrational [closed]

Prove that $\sqrt{\sqrt{5}+3}$ is irrational. What would be the easiest approach to this proof?
1
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1answer
33 views

Decide whether the following number is rational

Working needs to be shown $\sqrt{\sqrt{5}+3}+\sqrt{\sqrt{5}-2}$ My guess is to multiply by $\sqrt{\sqrt{5}+3}-\sqrt{\sqrt{5}-2}$ then we have a rational number but is it enough to prove the ...
0
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2answers
34 views

Parallel line with a known point

Line m goes through a point D(2, -4). Line m is parallel to line l: $5x+3y=-17$. Describe line m with an equation of type $ax+by=c$. The solution should be $c=5*2+3*-4=-2$ so $\text{m: }5x+3y=-2$ ...
0
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1answer
37 views

Irrationality proof

Prove that $\sqrt{7-\sqrt{2}} $ is irrational My idea is the following $\sqrt{7-\sqrt{2}} \in\mathbb{Q}$ $w^2=7+\sqrt{2}$ $w^2-7=\sqrt{2}$ thus w cannot be rational is this correct? edit: or ...
17
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3answers
225 views

What combinatorial quantity the tetration of two natural numbers represents?

Tetration is a generalization of exponentiation in arithmetic and a part of a series of other generalized notions, Hyperoperators. Consider $m\uparrow n$ denotes the tetration of $m$ and $n$. i.e. ...