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

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2answers
21 views

A number which can be expressed as the sum of the squares of 6 odd integers

Which one of the numbers below can be expressed as the sum of the squares of 6 odd integers? $${1998,1996,2000,2002,2004}$$ I first started this by saying if $m$ is odd then $m = 2k+1$ so $$m^2 = ...
0
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1answer
34 views

Rationalize a fraction using conjugates

I need help rationalizing the following expression using a conjugate: $$\dfrac{1}{\sqrt{3} + \sqrt{2}-\sqrt{5}}$$ I have had no luck rationalizing this expression with a conjugate of the ...
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2answers
33 views

Conjugates of radicals

I am not sure if one exists but is there a conjugate of the following: $$\sqrt{3}+\sqrt{2}-\sqrt{5}$$ I attempted it many times but can't get anything.
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1answer
15 views

What expression represents the total cost?

A customer calculated the cost of a new jacket , c, including a 7% sales tax, by multiplying 0.07 times the cost of the jacket and adding the product to the cost of the jacket. What is another way to ...
0
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0answers
5 views

Addition of two box plots

I have two box plots that I'd like to add together to form one box plot representing both plots in one. Here's an example of two box plots: At a school 200 boys and 200 girls participated in a test. ...
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5answers
137 views

Algebra problem stumping me

I have recently run into an algebra problem that goes as follows. Using the digits $1$ to $9$, $$ \left\{ \begin{align} A + B + C + D &= EF \\ E + F + G + H &= CJ \\ B + G + J ...
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4answers
955 views

Does the negative apply before or after an exponent

I have been having an argument with a friend, and they claim $-8^0$ is $1$, and I claim that $-8^0$ is really $-(8^0)$ and is therefore $-1$. Who is right?
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1answer
29 views

Another fascinating number chain!!

Take any two digit number none of whose digit is $0$. Now add the product of the digits in that number. if number becomes three digit number take last two digits. you will find a chain of numbers or a ...
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2answers
33 views

Solution to this problem?

Could you solve this question for me? If $10$ years are added to $3/5$ of the age of John, he will be $4$ years younger to the present age of his elder brother who will be $25$ years. What is the ...
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2answers
39 views

What is the remainder when $r+s$ is divided by 8? [on hold]

If $r$ and $s$ are integers greater than 1, and $11(s – 1) = 13(r – 1)$, then what is the remainder when $(r + s)$ is divided by 8?
2
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1answer
37 views

Formula for this pattern

I am trying to develop a computer program to compute the tax for a given base salary, I believe given the format of the income tax table that I have there should be a formula to calculate the tax for ...
1
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1answer
50 views

Why ${(a^2)}^{\frac 12}=\sqrt {a^2}=|a| \neq a$?

Let $a\in \mathbb R$. It should be true that $\sqrt {a^2}=|a|$, since $\sqrt {(-2)^2}=\sqrt{2^2}=2$ and so on. But, it is also true that ${(a^2)}^{\frac 12}=a$, and by definition, ${(a^2)}^{\frac ...
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1answer
24 views

question about division algorithm described in handbook of applied crypto

http://cacr.uwaterloo.ca/hac/about/chap14.pdf#page=9 gives the following as a division algorithm: So step 1 is making it so that $yb^{n-t}$ is the same length as x and then step 2 loops until the ...
-1
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0answers
39 views

Solve a CS related problem

This problem is a more advance version of this one: Solve this problem? ...
-1
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0answers
40 views

Calculated by multiplying the arithmetic progression terms

$$\prod_{k=1}^n(a+(k-1)d)=a\cdot(a+d)\cdot(a+2d)\cdot(a+3d)\cdots(a+(n-1)d)=\text{?}$$ Please help me! What is the formula?
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3answers
45 views

Quadratic equations and inequalites

For every positive integer $n$, prove that $$\sqrt{4n+1}<\sqrt{n} + \sqrt{n+1}<\sqrt{4n+2}$$ Hence or otherwise, prove that $[\sqrt{n}+\sqrt{n+1}] = [\sqrt{4n+1}]$, where $[x]$ ...
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votes
2answers
64 views

What would be the problem in mathematics if there are no negative numbers in number line? [on hold]

We all know that $-\times-=+$, $+\times+=+$ and $+\times-=-$. $-\times-$ will mean add a negative number, say, $-a$, $-a$ times, which is going out of sense. Other two are easy to understand, add ...
0
votes
2answers
65 views

What is the name of this summation formula?

So recently I derived a formula (obviously not the first... it already existed but that is what got me into summations) that quickly adds all the numbers from 1 to "n" However I recently derived ...
0
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4answers
50 views

A seemingly basic PEMDAS problem… [duplicate]

There's one of those meme-type images posted on Facebook with the equation 6/2(1+2), challenging you to solve it. So, parenthesis first, ...
4
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3answers
185 views

Mental Math Techniques [closed]

What are some interesting mental math techniques that you know? Here's one that I got from my Grandmother who got it from a book: To square a two-digit number (from $26$ to $49$), take the number ...
0
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2answers
42 views

Fastest way to do large additions?

In our book, in the statistics chapter, we have to add a large amount of numbers, especially for finding the mean of some given numbers. Most of the students in our class can do it easily in <30 ...
0
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0answers
38 views

Year to go calculation [closed]

After two months of sales a company sold 190 000 dollars and the last month is 95 000 dollars. The budget for the remaining of the year is 1 260 000. Consequently the company needs to do an average of ...
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0answers
12 views

An arithmetic sequence question

An arithmetic sequence question. The sum of the first nth term of the series is 2750. a) Show that n is given by n^2-15n=55x40 b) Hence find the value of n
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2answers
34 views

probability: arithmetic with random variables.

I have a question of using arithmetic on random variables. Please refer to the following question, to which I will present my solution using the arithmetic (which I thought it's correct but actually ...
0
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1answer
31 views

Simple binary subtraction with decimals

so let's say I am trying to subtract 75.442 by 43.646. I have 43.646 = 00101011.1010, and 75.442 = 01001011.0111 from 2's ...
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0answers
21 views

Help in approaching this question

Mark and his classmates were playing a game called “last man standing”. The last person left would have to be treated by the rest. The game went like this. From among $n$ of his classmates, numbered ...
0
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0answers
41 views

How to solve this question/approach to solve this question?

A family tree of the Royal Family of Mysore has n vertices to represent each of its members. The present king, who is also the oldest member of the family, decides to find his heir. He decides that ...
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1answer
63 views

so Thinking about induction proofs

So I'm studying some induction proofs, but I have some questions that were not clear to me when I read the book's definition. I want to know if my understanding is correct: So, for me, and ...
1
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1answer
34 views

Why isn't the zero after the decimal in $0.01$ significant?

Why isn't the zero after the decimal in $0.01$ significant? Although it is pretty obvious that the zero before the decimal is insignificant, I don't understand why the zero after the decimal is not ...
2
votes
1answer
26 views

Intuition for rules of rounding numbers

My textbook says that while rounding a number, if the digit next to the digit to be rounded is a 5, then increment the digit to be rounded by 1 if it is even odd, else do not increase. I don't ...
3
votes
1answer
48 views

Calculate the summation of double continued fractions

A few month ago, my brother had given me this question: \begin{equation} \cfrac{1}{2 + \cfrac{1}{3 + \cfrac{1}{4 + \cfrac{1}{\cdots+\frac{1}{2005}} } } }+\cfrac{1}{1 + ...
0
votes
2answers
47 views

Is there a simple algorithm for exponentiating large numbers to large powers?

I've been thinking about this for some days, a multiplication is a lot of sums, so: $$75\times 75=\overbrace{75+75+75+75+75+75+75+75+\cdots}^{\text{75 times}}$$ But then, there is a simple algorithm ...
2
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1answer
44 views

How to convert base 7 to base 19 directly

Is it possible to convert base 7 to base 19 directly without first converting to base 10 ? If so, what is the algorithm ?
2
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2answers
88 views

number of terms

The following problem maybe tedious if done by hand and requires patience. After factorizing the following variables find the number of terms and the sum of the number of terms. ...
2
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3answers
47 views

proof by contradiction that if a and b are positive integars and $ab >100$ then at least one of the integars a and b is greater than 10 [closed]

does anyone know how to proof by contradiction that if $a$ and $b$ are positive integars and $ab >100$ then at least one of the integars $a$ and $b$ is greater than $10$
2
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5answers
51 views

For any prime $p>3$ show that 3 divides $2p^2+1$

Does anyone know how to show this preferable without using modular For any prime $p>3$ show that 3 divides $2p^2+1$
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4answers
44 views

Show that if $p$ is a prime number $> 3$ then $24 \mid p^2-1$ [duplicate]

Hi guys can someone help me with this ?(Without using Modular arithmetic) Show that if $p$ is a prime number $>3$ then $24$ $\mid$ $p^2-1$
6
votes
3answers
69 views

Show that $9\mid a^2$ if given that $6\mid a$

Does this prove I made seem correct to show that if $6$ divides $a$ then $9$ divides $a^2$ If $6\mid a$, then $a = 6k$ (k is some integer). Then $a^2 = 36k^2 = 9(4k^2)$. Which means that $9\mid ...
0
votes
1answer
49 views

Explain theorem in Number theory

can some one explain with a clear example this theorem for me, Let ($A_1$, $A_2$, $A_3$,..., $A_n$) be integars and $p$ a prime number. if $p|(A_1A_2A_3...A_n)$ then there exist some $1 \leq k \leq ...
0
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0answers
14 views

Is there a program for convenient working with equations and coefficients?

I perform some calculations with one differential equation. Then I got a huge expression depending on $x$ and its degrees/powers. E.g. $$\alpha x+(4-x+\sqrt[3]{x})^2-(\beta\sqrt{x}+\frac12(x^3+1))^3 + ...
0
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2answers
33 views

What does P(A U B) mean, in terms of real values?

I can't find a proper summary or reference of how to translate formulas in probability notation to arithmetic notation (i.e. when using real values). For example, if $P(A) = .7$ and $P(B)=.35$, what ...
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2answers
79 views

What does this equal? $6\div 2(1+2)$

How do you figure out what $$6\div 2(2+1)$$ is equal? I get $9$, but some people say $7$ or even $1$ and I don't know how they get that? What does it really equal?
2
votes
1answer
23 views

multiplication problem of assigning numericals

I don't fully understand multiplication: $1*1=1$, $2*1=2$ and $0*1=0$ etc... But it would seem $3*2=6$ and not $3$? The first number is usually assigned as the result of the multiplication, but in the ...
0
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1answer
26 views

Geometric Progression related question.

In a sequence, first term a1 = 100 and nth term, an = 100 + (an-1)/5 If for some integer k, a50 lies between k and (k + 1), then k =
0
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2answers
27 views

How can we prove this = 1 for all n

$\displaystyle n!-\sum_{k=1}^{n-1}k\cdot k!$ By computing this by hand for several small values of $n$ I can see that it is always equal to 1. But I can't see how to prove that.
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3answers
51 views

Factoring added factorials

How do I facilitate prime factorization without brute-forcing the 600+ digit number? For example, how would I factor (82! + 83! + 84!) ?
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3answers
63 views

Could the fourth root of $1$ be $i$?

Could the fourth root of $1$ be $i$ (or $-i$)? I could show this by doing: $\sqrt[4]{1}$ $\sqrt{\sqrt{1}}$ $\sqrt{\pm{1}}$ $\sqrt{1}$ OR $\sqrt{-1}$ $\pm1$ OR $\pm i$ $\{1, -1, i, -i\}$ Would you ...
1
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1answer
52 views

Relations between $\sqrt x$ and $\sqrt{x+n}$

Is there any relation between $\sqrt x$ and $\sqrt{x+n}$? I am interested in the fractional part mostly. n and x are both positive integers, n is much greater than x.
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2answers
41 views

Is an anomaly in base-n arithmetic discoverable in base-m arithmetic?

I have always been fascinated by the book "Contact" by Carl Sagan. The final chapter of the book (not the film!) reports about an anomaly in the n-millionth decimal of pi, optimally visible when pi is ...
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1answer
47 views

Remainder of $1946^{1972} : 26$

Is this correct? $1946^1 = 22 \mod{26}$ $1946^2 = 22^2 = 484 = 16\mod{26}$ $1946^3 = 22^2 * 22 = 16 * 22 = 14 \mod{26}$ $1946^4 = 22^2 * 22^2 = 16^2 = 22 \mod{26}$ And therefore for any integer ...