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

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1answer
38 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
32 views

A seemingly basic PEMDAS problem…

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, ...
2
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3answers
86 views

Mental Math Tricks [on hold]

What are some interesting mental math tricks 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 minus ...
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2answers
39 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
36 views

Year to go calculation [on hold]

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 ...
-1
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0answers
11 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
27 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 ...
0
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0answers
19 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
40 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 ...
1
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1answer
62 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 ...
-3
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0answers
74 views

Help in solving this question [on hold]

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 1, ...
1
vote
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
41 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
41 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
85 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
50 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 $2p^2+1$
1
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4answers
42 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
68 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 ...
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0answers
13 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
votes
2answers
30 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
78 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
26 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!) ?
0
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3answers
62 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 ...
0
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1answer
44 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 ...
1
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1answer
23 views

A characterization of recursive functions via arithmetical formulas

Let $\mathcal{L}_A$ be the first order language of arithmetic with $+,\times,S$ and $0$. Let $\mathfrak{N}$ be the standard model of arithmetic. An $n$-ary relation $R$ on natural numbers is said to ...
0
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1answer
18 views

Expressing a open-high-low-close price series on standard basis

Say I have some stock-price time series expressed as follows: ...
0
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0answers
25 views

Euclidean algorithm to find GCD

I have to find GCD(975, 442) using Euclidean algorithm and write it in like: $ax + by$. Please tell me what do i do wrong. ...
0
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0answers
36 views

An isosceles triangle with a measure of the sides abc of $5,5$ and $4$.

Find the angles of the triangle in an isosceles triangle of length 5 as the hypotenuse and $\sqrt{21}$ as the height of the triangle as well as the angle bisector, and measure the angles and find ...
0
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2answers
34 views

Help on this divisibility Problem

Find all positive integers m and n such that: $$ m+n\mid mn+1 $$ we have according to the condition $$ m+n\mid (m+1)(n+1) $$ any ideas??
0
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1answer
20 views

Explanation and validation of point adding/doubling on elliptic curves

I'd like to implement point multiplication on elliptic curves over prime fields. My problem is that I've found different definition how to do it. At adding: the second parameter of the result is not ...
2
votes
1answer
29 views

How to find the multiplication of $pq \times abc$ such that the result is producing the same digits from the original problem?

For example: $$65 \times 281= 18265$$ $$65 \times 983= 63895$$ $$72 \times 936= 67392$$ $$87 \times 435= 37845$$ In general: the original figures reappear in the results of each of these ...
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1answer
26 views

Find the lightest one [closed]

There are nine balls. One is slightly lighter than the rest; the difference is small enough that you can't tell just by picking them up. Using a basic two-sided scale, what's the minimum number of ...
10
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3answers
352 views

Is calculation a part or just a result of Mathematics?

There is a question that came to my mind that I'd like to discuss here. I hope it is clear what I want to express since English is not my mother tongue. Since I have started studying mathematics and ...
0
votes
1answer
47 views

Is there a term for this subtraction formula?

Is there a term for this concept? Any link? n is a decimal from 0 to 1, including FORMULA n = 0.5 x = 1 - n EXAMPLES ...
0
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1answer
30 views

How to prove that both of them are the same?

$$ 3^{n+1}-2^{n+1} = \left [ 38\cdot 2^{n-3}+ \sum_{i=3}^{n}\left ( 2^{n-i}\cdot 3^{i} \right ) \right ],n\geq 3 $$ I had a college entrance exam few days ago, and I checked my answer with others. ...
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3answers
52 views

Number of 0 in great number

For example, 11111111111111100 ends with 2 zeros ,when we did know the decimal representation like 100! also. I would like a justified answer for the following question . How many 0 are in the end ...
2
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1answer
39 views

consecutive prime power

I'm interesting on consecutive prime power numbers. I see that there is the Mersenne primes and the Fermat Primes that give solutions and $(8,9)$. In Sloane collection it is referred on A006549 and it ...
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1answer
41 views

I need to do math from ground up, so what is a good workbook?

Can you guys recommend me a workbook that begins with arithmetic and ends with calculus. Or from pre-algebra to calculus. Like all "Master Math Series" books but in one complete book. It would really ...
4
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3answers
73 views

What does multiplication mean in probability theory?

For independent events, the probability of both occurring is the product of the probabilities of the individual events: $Pr(A\; \text{and}\;B) = Pr(A \cap B)= Pr(A)\times Pr(B)$. example: if you ...
2
votes
1answer
39 views

Smallest integer greater than the given number

What is the smallest integer greater than the real number $(\sqrt{5}+\sqrt{3})^{2n}$ (for non-negative integer $n$)? The answer is $(\sqrt{5}+\sqrt{3})^{2n}+(\sqrt{5}-\sqrt{3})^{2n}$. I just checked ...