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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13
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4answers
1k 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?
0
votes
1answer
48 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 ...
1
vote
2answers
44 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 ...
2
votes
1answer
92 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 ...
2
votes
1answer
79 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 12}=\...
1
vote
1answer
59 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
vote
3answers
54 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 $[x]$ ...
0
votes
2answers
85 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
votes
4answers
295 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, ...
5
votes
3answers
433 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
votes
2answers
83 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
votes
2answers
195 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 ...
1
vote
1answer
51 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 ...
1
vote
1answer
70 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
vote
1answer
126 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 ...
3
votes
1answer
65 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 ...
4
votes
1answer
130 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
96 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
votes
1answer
155 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
votes
2answers
217 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. $(a^0),(a+b)^0,(a+b+c)...
2
votes
3answers
61 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 $10$
1
vote
5answers
70 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
vote
4answers
135 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
89 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 $9\mid a^2$...
0
votes
1answer
61 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 ...
1
vote
3answers
15k 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 ...
0
votes
2answers
154 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?
3
votes
4answers
74 views

What is the value of $ 2013-2009+2005-2001 + \cdots + 29-25 $?

Calculate the value of: $$ 2013-2009+2005-2001 + \cdots + 29-25 $$ Ok I tried to answer this first by arranging the numbers: $$ (2013-2009)+(2005-2001)+ \cdots + (29-25) $$ so that the answer in each ...
0
votes
1answer
47 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
votes
2answers
32 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.
1
vote
3answers
97 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
votes
2answers
101 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
vote
1answer
59 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.
0
votes
2answers
122 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
votes
1answer
55 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
vote
1answer
41 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 ...
1
vote
1answer
80 views

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

Say I have some stock-price time series expressed as follows: ...
0
votes
2answers
41 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
votes
1answer
46 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
36 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 ...
1
vote
2answers
43 views

Question about something I found in a proof

I came across in a proof I was reading in my textbook that $ab - a'b' = ab - ab' + ab' - a'b'$. I was wondering why/how that equality is true.
12
votes
3answers
468 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
55 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
votes
1answer
56 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. ...
0
votes
3answers
85 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 ...
3
votes
3answers
89 views

Show that $\frac{1}{2 \sqrt{n+1}}\le \sqrt{n+1} - \sqrt{n} \le \frac{1}{2 \sqrt{n}} $

I actually would just like a bit of assistance in understanding a step in the solution. I'm just finding it a bit hard to see how the teacher jumped from one step to one step, if someone could spell ...
2
votes
1answer
169 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 ...
1
vote
1answer
69 views

Different results from adding tax to each item's price versus adding it to the total

The math problem I encountered which is a bit of an anomaly is this : Suppose you are producing an invoice for a customer, and all items for that invoice are stored in a list (without taxes pre-...
1
vote
1answer
92 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 ...
7
votes
5answers
1k 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 ...